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DECIDABLE MODELS OF ω-STABLE THEORIES

2014
*
Journal of Symbolic Logic (JSL)
*

In particular, we show that for a countable ω-stable T, every countable

doi:10.1017/jsl.2013.2
fatcat:w3463o6xjrdulj2ia7drhlyw3y
*model*of T admits a decidable*presentation*if and only if all n-types in T are*recursive*and T has only countably many countable ... We characterize the ω-stable theories all of whose countable*models*admit decidable*presentations*. ... Let T be a*recursive*ω-stable theory with countably many countable*models*. Let M be a*model*of T . Then M has a decidable*presentation*if and only if all types realized in M are*recursive*. ...##
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Towards a theory of abstract data types: A discussion on problems and tools
[chapter]

1980
*
Lecture Notes in Computer Science
*

countable

doi:10.1007/3-540-09981-6_4
fatcat:vqke4bgb7bbkhltzioe4utian4
*models*. ... This paper aims to show that, in order to capture a quite relevant feature such as the*recursiveness*of abstract data types,*Model*Theory works better than Category Theory. ... Th.5.5 -There are axiomatizable theories without*recursive**models*and with infinitely many non isomorphic and non*recursive**prime**models*. ...##
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Recursive spectra of strongly minimal theories satisfying the Zilber trichotomy
[article]

2012
*
arXiv
*
pre-print

are

arXiv:1104.4666v3
fatcat:sezphceo4bcnblkfyh74qbosri
*recursively**presentable*; none of them are*recursively**presentable*; or only the zero-dimensional*model*of T is*recursively**presentable*. ... We conjecture that for a strongly minimal theory T in a finite signature satisfying the Zilber Trichotomy, there are only three possibilities for the*recursive*spectrum of T: all countable*models*of T ... Corollary 4.6. • The quasiendomorphism ring has a*recursive**presentation*. • acl(∅) is a Σ 1 subset of U . • The*prime**model*of T has a*recursive**presentation*. Proof. ...##
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Recursive spectra of strongly minimal theories satisfying the Zilber Trichotomy

2014
*
Transactions of the American Mathematical Society
*

are

doi:10.1090/s0002-9947-2014-05897-2
fatcat:otoxtwbouvhqzjrvapsyglgf7i
*recursively**presentable*; none of them are*recursively**presentable*; or only the zero-dimensional*model*of T is*recursively**presentable*. ... We conjecture that for a strongly minimal theory T in a finite signature satisfying the Zilber Trichotomy, there are only three possibilities for the*recursive*spectrum of T : all countable*models*of T ... Corollary 4.6. • The quasiendomorphism ring has a*recursive**presentation*. • acl(∅) is a Σ 1 subset of U . • The*prime**model*of T has a*recursive**presentation*. Proof. ...##
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Page 6025 of Mathematical Reviews Vol. , Issue 2000i
[page]

2000
*
Mathematical Reviews
*

We show that if C is any infinite

*recursive*field, it has a weak*presentation*which is not extendible to a*recursive**presentation*of any field containing C.” ... Andrey Morozov (Novosibirsk) 2000i:03050 03C57 03D45 12L12 Shlapentokh, Alexandra (1-ENC; Greenville, NC) Weak*presentations*of fields not extendible to*recursive**presentations*. ...##
###
MODELS OF THE FUNDAMENTAL THEOREM OF ARITHMETIC

1963
*
Proceedings of the National Academy of Sciences of the United States of America
*

by

doi:10.1073/pnas.50.4.604
pmid:16578551
pmcid:PMC221233
fatcat:6voa3l5clbaslezy2ubxbz5efe
*primes*alone as with the author's mosaic*model*of FTA given above) and a mixed form (in which a*model*is determined, in general, by both*primes*and composites as with the standard Gaussian model5). ... Clearly there cannot be a "pure" composite*model*, since, by hypothesis, every*model*of FTA contains at least one*prime*. Thus, the scheme of three forms exhausts all*models*of FTA. ...##
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Page 45 of Mathematical Reviews Vol. 53, Issue 2
[page]

1977
*
Mathematical Reviews
*

The authors investigate those

*prime*and universal*models*of complete decidable theories that have*recursive**presentation*(perhaps constructible or strongly constructible). ... Corollary 5.2: There exists a decidable totally transcendental theory whose only con- structible*model*is a*prime**model*. ...##
###
Negation and aggregates in recursive rules: the LDL++ approach
[chapter]

1993
*
Lecture Notes in Computer Science
*

The problem of allowing non-monotonic constructs, such as negation and aggregates, in

doi:10.1007/3-540-57530-8_13
fatcat:rbjr2ebflnfdfbdcjpeklyxbma
*recursive*programs represents a di cult challenge faced by current research in deductive databases. ... A novel and general treatment of set aggregates, allowing for user-de ned aggregates, is also*presented*. ... Given an XY-clique, Q, its*primed*version Q 0 , is constructed by*priming*certain occurrences of*recursive*predicates in*recursive*rules as follows: X-rules: all occurrences of*recursive*predicates are ...##
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Generalisation of recursive doubling for AllReduce: Now with simulation

2017
*
Parallel Computing
*

Using our method,

doi:10.1016/j.parco.2017.08.004
fatcat:fdt2tsusivhb3etps67mnkxq4y
*recursive*multiplying, we show reductions in execution time of between 8% and 40% of AllReduce on a Cray XC30 over*recursive*doubling. ... Using a custom simulator we further explore the dynamics of*recursive*multiplying. ... Section 3*presents*two*models*used to analyse the AllReduce operation in the context of message pipelining. The*recursive*multiplying algorithm is*presented*in Section 4. ...##
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Page 1574 of Mathematical Reviews Vol. , Issue 2003C
[page]

2003
*
Mathematical Reviews
*

*prime*submodels of the

*model*M. ... Two of them are that each element of a

*model*belongs to at least one minimal

*prime*submodel and that two different minimal

*prime*submodels can have at most one element in common. ...

##
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Neutrally Expandable Models of Arithmetic
[article]

2017
*
arXiv
*
pre-print

We show that cofinal extensions of

arXiv:1712.06503v1
fatcat:vjlkes252bfnhdjj6t6itulrjy
*prime**models*are neutrally expandable, and ω_1-like neutrally expandable*models*exist, while no*recursively*saturated*model*is neutrally expandable. ... A subset of a*model*of PA is called neutral if it does not change the dcl relation. A*model*with undefinable neutral classes is called neutrally expandable. ... Acknowledgements Jim Schmerl's comments on a preliminary version of this paper allowed us to improve some of the results and the overall*presentation*. Thank you Jim. ...##
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Page 4719 of Mathematical Reviews Vol. , Issue 87i
[page]

1987
*
Mathematical Reviews
*

Millar, Terrence (1-WI)

*Prime**models*and almost decidability. J. ... Theorem 1: There is a complete decidable theory with a*prime**model*that is not almost decidable. ...##
###
The new book of prime number records

1996
*
Computers and Mathematics with Applications
*

Peano

doi:10.1016/s0898-1221(96)90243-6
fatcat:enbe7ontunhcdfw7ewk4xodsna
*models*and primitive*recursion*. 5. Induction*models*. 6. Induction*models*and primitive*recursion*in induction*models*. IV. Frames and general structures. 1. Introduction. 2. ... Equational*presentation*of the functional theory of finite types. VI. Many-sorted logic. 1. Introduction. 2. ...##
###
Learning (through) recursion

2010
*
Proceedings of the fifteenth annual conference on Innovation and technology in computer science education - ITiCSE '10
*

However, a consistent

doi:10.1145/1822090.1822136
dblp:conf/iticse/Mirolo10
fatcat:ia7fvjrhy5dj7dvw4lrlby5nt4
*model*of*recursive*computations, although implied by the ability to use*recursion*in problem-solving, does not seem to be sufficient for the achievement of higher-level skills. ... In essence, my investigation lends further support to previous related findings on mental*models*. ... However, you are playing a game and you are not allowed to enter directly the expression (co-*primes*? x y); you can use co-*primes*? ...##
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The challenger launch decision: Risky technology, culture, and deviance at NASA

1996
*
Computers and Mathematics with Applications
*

Peano

doi:10.1016/s0898-1221(96)90247-3
fatcat:vk6xdsaw6fhxlocwgsaxekgvmu
*models*and primitive*recursion*. 5. Induction*models*. 6. Induction*models*and primitive*recursion*in induction*models*. IV. Frames and general structures. 1. Introduction. 2. ... Equational*presentation*of the functional theory of finite types. VI. Many-sorted logic. 1. Introduction. 2. ...
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