Effective model theory: the number of models and their complexity

Effective model theory: the number of models and their complexity (1999)

Cached

Download Links

by Bakhadyr Khoussainov , Richard A. Shore

Venue:	MODELS AND COMPUTABILITY
Citations:	13 - 5 self

BibTeX

@INPROCEEDINGS{Khoussainov99effectivemodel,
    author = {Bakhadyr Khoussainov and Richard A. Shore},
    title = {Effective model theory: the number of models and their complexity},
    booktitle = {MODELS AND COMPUTABILITY},
    year = {1999},
    pages = {193--239},
    publisher = {University Press}
}

Years of Citing Articles

Bookmark

OpenURL

Abstract

Effective model theory studies model theoretic notions with an eye towards issues of computability and effectiveness. We consider two possible starting points. If the basic objects are taken to be theories, then the appropriate effective version investigates decidable theories (the set of theorems is computable) and decidable structures (ones with decidable theories). If the objects of initial interest are typical mathematical structures, then the starting point is computable structures. We present an introduction to both of these aspects of effective model theory organized roughly around the themes of the number and types of models of theories with particular attention to categoricity (as either a hypothesis or a conclusion) and the analysis of various computability issues in families of models.

Citations

100	Model Theory, Encyclopedia of Mathematics and its Applications 42 - Hodges - 1993
43	Model Theory, Third edition - Chang, Keisler - 1990
40	On the degrees less than 0 - Sacks
26	1989], Generic copies of countable structures - Ash, Knight, et al.
26	Recursively Presentable Prime Models - Harrington - 1974
23	Computably Categorical Structures and Expansions by Constants - Cholak, Goncharov, et al.
22	1979], ‘Effective content of field theory - Metakides, Nerode
21	Computable Isomorphisms, Degree Spectra of Relations and Scott Families, Annals of Pure and Applied Logic 93 - Khoussainov, Shore - 1998
20	1981], ‘Recursive isomorphism types of recursive Boolean algebras - Remmel
19	Effective model theory vs. recursive model theory - Chisholm
19	The Possible Turing Degree of the Nonzero Member in a two Element Degree Spectra, Annals of Pure and Applied Logic 55 - Harizanov - 1991
19	Foundations of recursive model theory - Millar - 1978
19	Recursive categoricity and persistence - Millar
18	Recursively Categorical Linear Orderings - Remmel
14	1997], ‘Permitting, forcing and copying of a given recursive relation, Ann - Ash, Cholak, et al.
13	Intrisically recursive relations, Aspects of Effective Algebra - Ash, Nerode - 1981
12	Strongly Constructive Models of a Decidable Theory - Khisamiev - 1974
11	Pairs of recursive structures - Ash, Knight - 1990
11	Constructive models of complete decidable theories. Algebra i Logika - Goncharov, Nurtazin - 1973
11	An autostable 1-decidable model without a computable Scott family of 9-formulas, Algebra and Logic 35 - Kudinov - 1996
10	Recursive labelling systems and stability of recursive structures in hyperarithmetical degrees - Ash - 1986
10	1997], Computable models of theories with few models, Notre Dame - Khoussainov, Nies, et al.
10	1974], ‘Strong and weak constructivizations and computable families - Nurtazin
10	1950], An essentially undecidable axiom system - Robinson
9	1980a], ‘The problem of the number of nonautoequivalent constructivizations - Goncharov
9	Omitting Types, Type Spectrums, and Decidability - Millar - 1983
9	1959], Non-Archimedian models of arithmetic - Tennenbaum
8	1986a], Stability of recursive structures in arithmetical degrees - Ash
8	Relatively recursive expansions - Ash, Knight - 1992
8	Decidable Models - Morley
8	1976], Numerations of families of general recursive functions, Algebra and Logic 15 - Selivanov - 1976
6	Possible degrees in recursive copies - Ash, Knight - 1997
6	1973], ‘Constructivizability of superatomic Boolean algebras’ (Russian), Algebra i Logika 12, 31-40; translation in Algebra and Logic - Goncharov
6	1981], ‘Groups with a finite number of constructivizations - Goncharov
6	1997], ‘On the spectrum of the degrees of decidable relations - Goncharov, Khoussainov
6	1982], Techniques and Counterexamples in Almost Categorical Recursive Model Theory - Manasse
5	The complexity of intrinsically r.e. subsets of existentially decidable models - Chisholm
5	Nilpotent groups of finite algorithmic dimension’, Sib - Goncharov, Molokov, et al. - 1989
5	1980], Constructivizable models of undecidable theories - Kudaibergenov
5	Recursively represented Boolean algebras - LaRoche
4	Elementary theories and their constructive models, Handbook of Recursive Mathematics - Ershov, Goncharov - 1999
4	Strong constructivizability of homogeneous models - Goncharov - 1978
3	A completeness theorem for certain classes of recursive infinitary formulas - Ash, Knight - 1994
3	computable families of constructivizations’ (Russian), Algebra i Logika 14, 647–680; translation in Algebra and Logic - Goncharov
3	1980], ‘Autostability of models’ (Russian), Algebra i Logika 19, 45–58; translation in Algebra and Logic - Goncharov, Dzgoev
2	Limit equivalent constructivizations (Russian - Goncharov
2	Autostable models and their algorithmic dimension’, in Ershov et al - Goncharov - 1998
2	1979], A theory with two strongly constructible models (Russian), Algebra i Logika 18, 176--185, 253; translation in Algebra and Logic 18 - Kudaibergenov - 1979
2	Complete, decidable theory with two decidable models - Millar
2	1999], ‘Abstract recursive model theory - Millar