Freely Generated Projective Planes with Finite Computable Dimension

Kogabaev, N. T.

doi:10.1007/s10469-017-9418-9

Cited by 4 publications

(2 citation statements)

References 20 publications

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“…Known examples of

\mathit {DSED}

‐universal classes of structures include: (a)directed graphs, undirected graphs, partial orders, (non‐modular) lattices, rings (with zero‐divisors), integral domains of arbitrary characteristic, commutative semigroups, 2‐step nilpotent groups [18]; (b)fields of arbitrary characteristic [32]; (c)Pappian projective planes [26]; (d)freely generated projective planes [27]; (e)structures with two equivalence relations [31, 48]; (f)Boolean algebras with operators [22]; (g)polymodal algebras [2]; (h)contact algebras [3]. …”

Section: Universal Classes Of Structuresmentioning

confidence: 99%

On the effective universality of mereological theories

Bazhenov

Tsai

2021

Mathematical Logic Qtrly

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Mereological theories are based on the binary relation “being a part of”. The systematic investigations of mereology were initiated by Leśniewski. More recent authors (including Simons, Casati and Varzi, Hovda) formulated a series of first‐order mereological axioms. These axioms give rise to a plenitude of theories, which are of great philosophical interest. The paper considers first‐order mereological theories from the point of view of computable (or effective) algebra. Following the approach of Hirschfeldt, Khoussainov, Shore, and Slinko, we isolate two important computability‐theoretic properties P (namely, degree spectra of structures, and effective dimensions), and consider the following problem: for a given mereological theory T, is it true that its models can realize every possible variant of the property P? If the answer is positive, then we say that the theory T is DSED$\mathit {DSED}$‐universal. We obtain the following results about known mereological theories. Any theory T which is weaker than Extensional Closure Mereology (CEM) is DSED$\mathit {DSED}$‐universal. A similar fact is true for the theory GM2. On the other hand, any theory stronger that CEM + (C) + (G) is not DSED$\mathit {DSED}$‐universal. In particular, General Extensional Mereology is not DSED$\mathit {DSED}$‐universal.

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“…Known examples of

\mathit {DSED}

Section: Universal Classes Of Structuresmentioning

confidence: 99%

On the effective universality of mereological theories

Bazhenov

Tsai

2021

Mathematical Logic Qtrly

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“…The results of [66] imply that the following classes are complete with respect to effective dimensions: directed graphs, symmetric irreflexive graphs, partial orders, nondistributive lattices, rings (with zero-divisors), integral domains of arbitrary characteristic, commutative semigroups, 2-step nilpotent groups. Furthermore, completeness with respect to effective dimensions was established for the following classes: fields of zero characteristic [86], Pappian projective planes [69], freely generated projective planes [70], Boolean algebras with operators [68], polymodal algebras [16], and structures with two equivalence relations [77,99].…”

Section: Classes Complete With Respect To Categoricity Spectramentioning

confidence: 99%

Categoricity Spectra of Computable Structures

Bazhenov

2021

J Math Sci

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The categoricity spectrum of a computable structure S is the set of all Turing degrees capable of computing isomorphisms among arbitrary computable presentations of S. The degree of categoricity of S is the least degree in the categoricity spectrum of S. This paper is a survey of results on categoricity spectra and degrees of categoricity for computable structures. We focus on the results about degrees of categoricity for linear orders and Boolean algebras. We construct a new series of examples of degrees of categoricity for linear orders.

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Computable Heyting Algebras with Distinguished Atoms and Coatoms

Bazhenov

2022

J of Log Lang and Inf

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Freely Generated Projective Planes with Finite Computable Dimension

Cited by 4 publications

References 20 publications

On the effective universality of mereological theories

On the effective universality of mereological theories

Categoricity Spectra of Computable Structures

Computable Heyting Algebras with Distinguished Atoms and Coatoms

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