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An Interpretation of Robinson Arithmetic in its Grzegorczyk's Weaker Variant
The paper presents an interpretation of Robinson arithmetic in its weaker variant considered by A. Grzegorczyk, in which addition and multiplication are partial functions....
BA - Obecná matematika
- 2007 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
The Intuitionistic Robinson Arithmetic(s)
Heyting arithmetic HA is a well established intuitionistic theory. As a counterpart to Peano arithmetic PA, it forms the theory of constructive arithmetic. Its induction-less variant, the intuitionistic Robinson
AA - Filosofie a náboženství
- 2015 •
- D
Rok uplatnění
D - Stať ve sborníku
How Much Propositional Logic Suffices for Rosser's Undecidability Theorem?
and for a much weaker arithmetic theory, a version of Robinson’s R (with arithmetic be for Rosser’s essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson...
Pure mathematics
- 2022 •
- Jimp •
- Link
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
Výsledek na webu
Division by zero
For any sufficiently strong theory of arithmetic, the set of Diophantine equations provably unsolvable in the theory is algorithmically undecidable, as a consequence of the MRDP theorem. In contrast, we show decidability of Diophantine equat...
BA - Obecná matematika
- 2016 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Výsledek na webu
A weak theory of building blocks
We apply the mereological concept of parthood to the coding of finite sequences. We propose a first-order theory in which coding finite sequences is intuitive and transparent. We compare this theory with Robinson arithmetic, adjunct...
Pure mathematics
- 2024 •
- Jimp •
- Link
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
Výsledek na webu
Sequence encoding without induction
We show that the universally axiomatized, induction-free theory PA(-) is a sequential theory in the sense of Pudlak's [5], in contrast to the closely related Robinson's arithmetic....
BA - Obecná matematika
- 2012 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Výsledek na webu
Towards Metamathematics of Weak Arithmetics over Fuzzy Logic
This paper continues investigation of a very weak arithmetic that results from the well-known Robinson arithmetic by not assuming that addition and multiplication are total functions and, secondly, by weakening the classica...
BA - Obecná matematika
- 2011 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Výsledek na webu
Mathematical Fuzzy Logic and Natural Numbers
A weak variant of Robinson's arithmetic Q where the binary operations of addition and multiplication are replaced by ternary relations ( not necessarily fuzzy logic BL for all. Essential undecidability of this fuzzy arithmetic
BA - Obecná matematika
- 2007 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
On Interpretability in the Theory of Concatenation
The paper discusses the theory of concatenation TC, defined by A. Grzegorczyk. A proof that Robinson arithmetic Q is interpretable in TC is given....
BA - Obecná matematika
- 2008 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Weak Theories and Essential Undecidability
Weak variants Q-, R, and R_0 of Robinson arithmetic, and the theory of concatenation TC, and essential udecidability proofs of those are discusses. A proof of self-reference theorem for the theory R_0 is given....
BA - Obecná matematika
- 2008 •
- D
Rok uplatnění
D - Stať ve sborníku
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