Substitutions and Substitutability

[knowledge base]

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SUBSTITUTIONS, SUBSTITUTABILITY, and their underlying definitions are presented in this white paper (knowledge base).

https://doi.org/10.31219/osf.io/k6w7u

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 212, 2021 [II]

Model

[knowledge base]

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MODEL (mathematical logic) and its underlying definitions are presented in this white paper (knowledge base).

https://doi.org/10.31219/osf.io/vs6j9

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 209, 2021 [IF]

A unidimensional windmill in the plane with varying pivot points

[white paper]

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We show that we can choose a point in the plane such that the resulting windmill process with varying pivot uses each point of the plane infinitely many times.

https://doi.org/10.31219/osf.io/mwkaf

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 2, Article 148, 2020 [FT]

Logical Loop

[microresearch]

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We discuss the dubbed term “logical loop” and it’s implication regarding provability in undecidable theorems.

https://doi.org/10.31219/osf.io/c5ezm

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 2, Article 123, 2020 [ET]

Non-classical logic and undecidability

[conjecture]

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We elaborate a conjecture by applying the definition of Non-Axiomatic System [1] in Non-Classical Logic.

https://doi.org/10.31219/osf.io/h4f7p

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 2, Article 112, 2020 [EI]

The logic of entanglement in gravity

[microresearch]

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We explore the relation between gravity and entanglement using mathematical logic (Modus Ponens).

https://doi.org/10.31219/osf.io/m2dca

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 1, Article 58, 2019 [CF]

Hilbert-style proof Calculus for Propositional Logic in ABC notation

[microreview]

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All nine axioms and a single inference rule of logic (Modus Ponens) within the Hilbert axiomatic system are presented using capital letters (ABC) in order to familiarize the beginner student in hers/his first contact with the topic.

https://doi.org/10.31219/osf.io/jd3gp

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 1, Article 57, 2019 [CE]

The Incorrectness Lemma

[original idea]

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We address two questions. Is there an Incorrectness Lemma? Is this system complete?

https://doi.org/10.31219/osf.io/f8p7k

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 1, Article 53, 2019 [CA]

A pedagogical approach to convert “if and only if” to “if then”

[microreview]

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We show, using the equivalence of some formulas, that (A iff B) ~ ((A v B) => (A ^ B)).

https://doi.org/10.31219/osf.io/xhzc9

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 1, Article 52, 2019 [BZ]

Generalized Pierce law

[microresearch]

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An extension of the Pierce law is presented, considering n “if then” connectives.

https://doi.org/10.31219/osf.io/6fbgp

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 1, Article 50, 2019 [BX]

Gödel’s incompleteness theorem in a nutshell

[microreview]

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We present a microversion of Gödel’s theorem.

https://doi.org/10.31219/osf.io/gphsk

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 1, Article 45, 2019 [BS]

Vacuously true sentences: Are they non-Boolean and undecidable?

[microresearch]

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We propose a discussion on the non-Boolean mathematical object embedded in vacuously true sentences.

https://doi.org/10.31219/osf.io/8r3j2

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 1, Article 35, 2019 [BI]