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DECIDABLE MODELS OF ω-STABLE THEORIES

URI ANDREWS
2014 Journal of Symbolic Logic (JSL)  
In particular, we show that for a countable ω-stable T, every countable 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.  ... 
doi:10.1017/jsl.2013.2 fatcat:w3463o6xjrdulj2ia7drhlyw3y

Towards a theory of abstract data types: A discussion on problems and tools [chapter]

A. Bertoni, G. Mauri, P. Miglioli
1980 Lecture Notes in Computer Science  
countable 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.  ... 
doi:10.1007/3-540-09981-6_4 fatcat:vqke4bgb7bbkhltzioe4utian4

Recursive spectra of strongly minimal theories satisfying the Zilber trichotomy [article]

Uri Andrews, Alice Medvedev
2012 arXiv   pre-print
are 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.  ... 
arXiv:1104.4666v3 fatcat:sezphceo4bcnblkfyh74qbosri

Recursive spectra of strongly minimal theories satisfying the Zilber Trichotomy

Uri Andrews, Alice Medvedev
2014 Transactions of the American Mathematical Society  
are 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.  ... 
doi:10.1090/s0002-9947-2014-05897-2 fatcat:otoxtwbouvhqzjrvapsyglgf7i

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

A. A. Mullin
1963 Proceedings of the National Academy of Sciences of the United States of America  
by 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.  ... 
doi:10.1073/pnas.50.4.604 pmid:16578551 pmcid:PMC221233 fatcat:6voa3l5clbaslezy2ubxbz5efe

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]

Carlo Zaniolo, Natraj Arni, Kayliang Ong
1993 Lecture Notes in Computer Science  
The problem of allowing non-monotonic constructs, such as negation and aggregates, in 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  ... 
doi:10.1007/3-540-57530-8_13 fatcat:rbjr2ebflnfdfbdcjpeklyxbma

Generalisation of recursive doubling for AllReduce: Now with simulation

Martin Ruefenacht, Mark Bull, Stephen Booth
2017 Parallel Computing  
Using our method, 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.  ... 
doi:10.1016/j.parco.2017.08.004 fatcat:fdt2tsusivhb3etps67mnkxq4y

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.  ... 

Neutrally Expandable Models of Arithmetic [article]

Athar Abdul-Quader, Roman Kossak
2017 arXiv   pre-print
We show that cofinal extensions of 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.  ... 
arXiv:1712.06503v1 fatcat:vjlkes252bfnhdjj6t6itulrjy

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 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.  ... 
doi:10.1016/s0898-1221(96)90243-6 fatcat:enbe7ontunhcdfw7ewk4xodsna

Learning (through) recursion

Claudio Mirolo
2010 Proceedings of the fifteenth annual conference on Innovation and technology in computer science education - ITiCSE '10  
However, a consistent 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?  ... 
doi:10.1145/1822090.1822136 dblp:conf/iticse/Mirolo10 fatcat:ia7fvjrhy5dj7dvw4lrlby5nt4

The challenger launch decision: Risky technology, culture, and deviance at NASA

1996 Computers and Mathematics with Applications  
Peano 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.  ... 
doi:10.1016/s0898-1221(96)90247-3 fatcat:vk6xdsaw6fhxlocwgsaxekgvmu
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