[30] **viXra:1904.0549 [pdf]**
*submitted on 2019-04-28 17:05:57*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate equations about adding or subtracting something from nothing. The duals as a disjunction are tautologous. However that disjunction is not itself equivalent to nothing. This refutes the Cabannas theory of objectivity at its atomic level, forming a non tautologous fragment of the universal logic VŁ4.

**Category:** Set Theory and Logic

[29] **viXra:1904.0526 [pdf]**
*submitted on 2019-04-27 23:38:01*

**Authors:** Colin James III

**Comments:** Pages.

Two definitions for expansion, remainder, and selection of K functions are not tautologous. Two definitions implication and paraconsistent/weak negation operators are not tautologous. These refute remainder sets and paraconsistent valuations of logic mbC, an extension of CPL+. Therefore these conjectures are non tautologous fragments of the universal logic VŁ4.

**Category:** Set Theory and Logic

[28] **viXra:1904.0516 [pdf]**
*submitted on 2019-04-26 10:24:51*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate collection theory as the set of universal closure of sentences in a schema equation. It is not tautologous. This refutes Collection as the conjectured schema. Therefore collection theory is a non tautologous fragment of the universal logic VŁ4.

**Category:** Set Theory and Logic

[27] **viXra:1904.0510 [pdf]**
*submitted on 2019-04-26 19:46:15*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

The precise definition of LPO and Ishihara’s tricks as rendered in four equations are not tautologous. This refutes LPO and Ishihara’s tricks. What follows is that (seemingly) impossible theorems in constructive mathematics are denied as theorems. Therefore those conjectures are non tautologous fragment of the universal logic VŁ4.

**Category:** Set Theory and Logic

[26] **viXra:1904.0493 [pdf]**
*submitted on 2019-04-25 13:17:26*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate five definitions as not tautologous. This refutes the conjecture that inductive-recursive definitions can give rise to ordinal notation systems that uniquely represent ordinals. Hence the definitions and conjecture are non tautologous fragment of the universal logic VŁ4.

**Category:** Set Theory and Logic

[25] **viXra:1904.0484 [pdf]**
*submitted on 2019-04-24 06:38:20*

**Authors:** Louiz Akram

**Comments:** 3 Pages.

This is a better scan of my work about riemann's hypothesis , I proved that there are no zeros when Re(s)<1 .
I didn't suppose that zeta is convergent , but I supposed that the zero is among the images with the relation zeta of a known s=a+ib since zeta is a relation when it doesn't converge.
There is an issue when we try to find an extension for Riemann's zêta : The complex form multiplied to zêta should never be null , because that form should also devide zêta to deduce the extension. The mistake is to multiply by a complex form then devide by only an image by it.
There is also the logical problem when zêta which is divergent equals a convergent extension. I think that suppositions should be made before trying to find an extension to Zeta.

**Category:** Set Theory and Logic

[24] **viXra:1904.0483 [pdf]**
*submitted on 2019-04-24 06:51:32*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

The definitions of directed, complete posets for antisymmetry and transitivity are not tautologous, thereby refuting basic domain theory. By extension, the Scott model of language PCF in univalent type theory is also refuted and another non tautologous fragment of the universal logic VŁ4.

**Category:** Set Theory and Logic

[23] **viXra:1904.0466 [pdf]**
*replaced on 2019-04-25 08:14:09*

**Authors:** Colin James III

**Comments:** 1 Page.

From the paper’s abstract, the definition of strong jump inversion is not tautologous, hence strong jump inversion is refuted. A computable enumeration of the types realized in models of DCF0 is also refuted. The alleged fact that the saturated model of DCF0 has a decidable copy is denied. Therefore these conjectures form a non tautologous fragment of the universal logic VŁ4.

**Category:** Set Theory and Logic

[22] **viXra:1904.0404 [pdf]**
*submitted on 2019-04-20 08:15:10*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate the subset equations for the basis of type theory. They are not tautologous. Therefore the basis of type theory is a non tautologous fragment of the universal logic VŁ4.

**Category:** Set Theory and Logic

[21] **viXra:1904.0385 [pdf]**
*submitted on 2019-04-19 12:16:13*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate a definition equation as not tautologous, hence refuting first order team (FOT) logics. Therefore FOT is a non tautologous fragment of the universal logic VŁ4.

**Category:** Set Theory and Logic

[20] **viXra:1904.0369 [pdf]**
*submitted on 2019-04-18 07:25:21*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

Huemer proposed a confirmation theory to solve the problem of induction. In lieu of the excess of content from Popper and Miller, the proposed replacement is also not tautologous, so we correct it for the intended use. That applied to the subsequent proposal in three parts shows one part is not tautologous, hence denying the proposal. Therefore Huemer’s confirmation theory is a non tautologous fragment of the universal logic VŁ4.

**Category:** Set Theory and Logic

[19] **viXra:1904.0365 [pdf]**
*submitted on 2019-04-18 08:26:57*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

Three equations of Parikh’s axiomatization of game logic G are not tautologous. Hence, the extended logic system Par is refuted, and Parikh’s completeness conjecture is also refuted. Therefore these artifacts are non tautologous fragments of the universal logic VŁ4.

**Category:** Set Theory and Logic

[18] **viXra:1904.0312 [pdf]**
*submitted on 2019-04-16 17:41:49*

**Authors:** Colin James III

**Comments:** Pages.

Two seminal rules of inference evaluated as not tautologous. This means the following are also refuted: Buss’s hierarchy of bounded arithmetics does not entirely collapse; Takeuti’s argument implies P ≠ NP; and systems PV and PV−. What follows is that separation of bounded arithmetic using a consistency statement is not viable. Therefore the above are non tautologous fragments of the universal logic VŁ4.

**Category:** Set Theory and Logic

[17] **viXra:1904.0311 [pdf]**
*submitted on 2019-04-16 22:13:42*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We confirm the definition that impossible worlds mean “nothing is necessary there but everything is possible”. The truth axiom as given is not tautologous, but rather the logical value of truthity. The rules of extensionality and monotonicity as given are not tautologous. When the definition of impossible worlds is combined with monotonicity + T + 4 that conjecture is also tautologous. Therefore the failed equations are non tautologous fragments of the universal logic VŁ4.

**Category:** Set Theory and Logic

[16] **viXra:1904.0292 [pdf]**
*submitted on 2019-04-15 10:26:51*

**Authors:** Colin James III

**Comments:** 3 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate the lemma proffered to prove Ramsey’s theorem, and the strengthened lemma in a note. Neither are tautologous. We evaluate the proof of Pythagorean triple of integers as colored. It also is not tautologous. In fact, the coloring or non-coloring produces a logically equivalent result, meaning the Ramsey theorem is neither a tautology nor a contradiction. This implies “the inductive hypothesis” is suspicious. What follows is that the HOL proof assistant for the Ramsey theorem is an historical enormity in its 200 TB computer program with a certified prize result. Therefore the Ramsey theorem and HOL proof assistants are non tautologous fragments of the universal logic VŁ4.

**Category:** Set Theory and Logic

[15] **viXra:1904.0290 [pdf]**
*submitted on 2019-04-15 11:33:56*

**Authors:** Colin James III

**Comments:** Pages.

We evaluate a seminal equation from a proof sketch, which is not tautologous. By extension, this means dependence logic, inclusion logic, and independence logic are also not tautologous. Therefore dependence logic, inclusion logic, and independence logic are non tautologous fragments of the universal logic VŁ4.

**Category:** Set Theory and Logic

[14] **viXra:1904.0284 [pdf]**
*submitted on 2019-04-15 20:35:54*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

An exemplary equation in HOL for ethical reasoning is not tautologous. By extension, HOL is refuted as “a universal meta-logic”, and “ethical reasoning” is refuted. Therefore HOL and ethical reasoning are non tautologous fragments of the universal logic VŁ4.

**Category:** Set Theory and Logic

[13] **viXra:1904.0182 [pdf]**
*replaced on 2019-04-22 06:07:09*

**Authors:** Colin James III

**Comments:** 2 Pages.

We evaluate Fodor’s principle in two versions we name weaker and stronger. Neither is tautologous. By extension, the class Fodor principle is not tautologous. Because of this, using Kelly-Morse set theory as a basis for denial is rendered moot. However, to rely on KM set theory to deny Fodor principles as a class principle is obviated by the refutation above. Therefore Fodor’s causality principles and extension are non tautologous fragments of the universal logic VŁ4.

**Category:** Set Theory and Logic

[12] **viXra:1904.0164 [pdf]**
*submitted on 2019-04-08 19:37:00*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

From a footnote, and then a three part definition, temporal type theory (TTT), and then temporal landscapes for open sets are not tautologous and hence refuted. That further refutes Scott’s topology. These results therefore form a non tautologous fragment of the universal logic VŁ4.

**Category:** Set Theory and Logic

[11] **viXra:1904.0148 [pdf]**
*submitted on 2019-04-07 09:55:15*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We assume the teacher is veracious and evaluate the assertion “There is possibly a quiz next week on Monday, Tuesday, or Wednesday.” It is not tautologous, hence denying it is a paradox and refuting it as a conjecture. Therefore the student quiz paradox is a non tautologous fragment of the universal logic VŁ4.

**Category:** Set Theory and Logic

[10] **viXra:1904.0145 [pdf]**
*submitted on 2019-04-07 17:06:59*

**Authors:** Farzad Didehvar

**Comments:** 6 Pages.

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzifying Turing Machines but seemingly there is no need to fuzzify time. Throughout this article, we try to change this picture and show why it is helpful to consider the instants of time as Fuzzy numbers.
In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it.
Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Paraconsistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time.

**Category:** Set Theory and Logic

[9] **viXra:1904.0129 [pdf]**
*submitted on 2019-04-06 14:00:21*

**Authors:** Tomonori Hirasa

**Comments:** 2 Pages.

The students in the surprise exam story reasoned that no surprise exam could take place on any day of the week. Actually, however, the students were surprised on Wednesday by the teacher's surprise exam. In this paper, we show where the students' reasoning went wrong and that students should be surprised on Wednesday or Tuesday.

**Category:** Set Theory and Logic

[8] **viXra:1904.0106 [pdf]**
*submitted on 2019-04-05 23:10:51*

**Authors:** Colin James III

**Comments:** Pages.

The clauses of the Malice and Alice logical puzzle of Summers are mapped for evaluation of the conjecture. It should return tautology for all pairwise answers, before removing pairs of the antecedent to discover the correct pair of murder and victim. However, the conjecture is not tautologous, albeit one value shy. This means the puzzle as rendered is not well formed, thereby denying the status of a puzzle. Therefore the conjecture is a non tautologous fragment of the universal logic VŁ4.

**Category:** Set Theory and Logic

[7] **viXra:1904.0101 [pdf]**
*submitted on 2019-04-04 06:03:04*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

The axiom of dependent choices (DC) is evaluated in two equations on supercompactness of ω1, with neither tautologous and hence refuting DC. Therefore DC equations are non tautologous fragments of the universal logic VŁ4.

**Category:** Set Theory and Logic

[6] **viXra:1904.0095 [pdf]**
*submitted on 2019-04-04 08:40:19*

**Authors:** Henry Wong

**Comments:** 3 Pages.

In propositional logic, given a set of axioms, we can derive formulas. Here we present the derivations of some formulas without the use of the Deduction Theorem. The derivations are presented compactly with only few referrals to other theorems. Most textbooks in this subject avoid this kind of approach.

**Category:** Set Theory and Logic

[5] **viXra:1904.0057 [pdf]**
*submitted on 2019-04-03 15:30:21*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate the example of mapping the Sahlqvist formula of p ∧ ◊p → ◻p into corresponding quantified expressions. The formula is not a theorem, but the corresponding quantified expressions are theorems. Hence the mapping refutes the Sahlqvist correspondence theory. Therefore these failures are non tautologous fragments of the universal logic VŁ4.

**Category:** Set Theory and Logic

[4] **viXra:1904.0050 [pdf]**
*submitted on 2019-04-03 21:49:58*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

"A Skolem axiom has the form ∀x,y(φ(x, y)→φ(x,f(x))), where f is a new function symbol introduced to denote a "Skolem function" for φ." The Skolem axiom form is not tautologous, hence refuting it. Therefore the Skolem axiom form is a non tautologous fragment of the universal logic VŁ4.

**Category:** Set Theory and Logic

[3] **viXra:1904.0043 [pdf]**
*submitted on 2019-04-02 10:36:44*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate the definition of ultrapower as a convention. The two states equated to 1 as designated proof value and as ordinal value are not tautologous. This refutes the ultrapower and hence colors the subsequent exposition to deny projective determinancy. Therefore the ultrapower and projective determinancy are non tautologous fragments of the universal logic VŁ4.

**Category:** Set Theory and Logic

[2] **viXra:1904.0027 [pdf]**
*submitted on 2019-04-02 22:53:17*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

From the fundamental axiom of ZF (or ZFC), ZF is proved contradictory. This means the method of forcing and the continuum hypothesis are also denied. Therefore these results are non tautologous fragments of the universal logic VŁ4.

**Category:** Set Theory and Logic

[1] **viXra:1904.0006 [pdf]**
*submitted on 2019-04-02 02:07:58*

**Authors:** Colin James III

**Comments:** 4 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

From one source we evaluate the Ackermann rule and from another source three examples in 15 equations of second-order reduction. None of the equations is tautologous. This implies these approaches to map modal clauses of first-order logic to and from second-order logic are non tautologous fragments of the universal logic VŁ4.

**Category:** Set Theory and Logic