Minimal models

1977 ◽  
Vol 42 (2) ◽  
pp. 254-260
Author(s):  
Rainer Deissler
Keyword(s):  
Upper Bound ◽  
Minimal Models ◽  
First Order ◽  
Elementary Submodel ◽  
Game Theoretic ◽  
Theoretic Characterization ◽  
Natural Way

A model is called minimal if it does not contain a proper elementary submodel. A class of models is called Σ11(Π11 resp. elementary) if it is axiomatized by a sentence with σ in and some string of predicate symbols. All languages considered are assumed to be countable. For each model we shall define in a natural way its rank, denoted by rk (), which is an ordinal or ∞. Intuitively speaking, rk () is the least upper bound for the number of steps needed to define the elements of by first order formulas; e.g. we shall have rk((ω, <)) = 1 (each element is f.o. definable), rk ((Z, <)) = 2 (no element is f.o. definable, each element is f.o. definable using any other element as a parameter), rk ((Q, <) ) = ∞ (no element is f.o. definable by any number of steps). This notion of rank leads to a useful game theoretic characterization of minimal models which we apply to show that the Π11 class of minimal models is not Σ11.

scholarly journals Game-theoretic characterization of antidegradable channels

2014 ◽  
Vol 55 (9) ◽  
pp. 092202 ◽  
Author(s):  
Francesco Buscemi ◽  
Nilanjana Datta ◽  
Sergii Strelchuk
Keyword(s):  
Game Theoretic ◽  
Theoretic Characterization

scholarly journals On the theorems of Y. Mibu and G. Debs on separate continuity

1996 ◽  
Vol 19 (3) ◽  
pp. 495-500 ◽  
Author(s):  
Zbigniew Piotrowski
Keyword(s):  
Continuous Functions ◽  
Game Theoretic ◽  
Theoretic Characterization

Using a game-theoretic characterization of Baire spaces, conditions upon the domain and the range are given to ensure a “fat” setC(f)of points of continuity in the sets of typeX×{y},y∈Yfor certain almost separately continuous functionsf:X×Y→Z. These results (especially Theorem B) generalize Mibu's. First Theorem, previous theorems of the author, answers one of his problems as well as they are closely related to some other results of Debs [1] and Mibu [2].

scholarly journals A game-theoretic characterization of Boolean grammars

2011 ◽  
Vol 412 (12-14) ◽  
pp. 1169-1183 ◽  
Author(s):  
Vassilis Kountouriotis ◽  
Christos Nomikos ◽  
Panos Rondogiannis
Keyword(s):  
Game Theoretic ◽  
Theoretic Characterization ◽  
Boolean Grammars

CONCURRENT AUTOMATA AND DOMAINS

1992 ◽  
Vol 03 (04) ◽  
pp. 389-418 ◽  
Author(s):  
MANFRED DROSTE
Keyword(s):  
Concurrent Systems ◽  
Equivalence Classes ◽  
Binary Relations ◽  
Transition Systems ◽  
Operational Model ◽  
Locally Finite ◽  
Natural Domain ◽  
Theoretic Characterization ◽  
Natural Way

We introduce an operational model of concurrent systems, called automata with concurrency relations. These are labeled transition systems [Formula: see text] in which the event set is endowed with a collection of symmetric binary relations which describe when two events at a particular state of [Formula: see text] commute. This model generalizes the recent concept of Stark’s trace automata. A permutation equivalence for computation sequences of [Formula: see text] arises canonically, and we obtain a natural domain [Formula: see text] comprising the induced equivalence classes. We give a complete order-theoretic characterization of all such partial orders [Formula: see text] which turn out to be particular finitary domains. The arising domains [Formula: see text] are particularly pleasant Scott-domains, if [Formula: see text] is assumed to be concurrent, i.e. if the concurrency relations of [Formula: see text] depend (in a natural way) locally on each other, but not necessarily globally. We show that both event domains and dI-domains arise, up to isomorphism, as domains [Formula: see text] with well-behaved such concurrent automata [Formula: see text]. We introduce a subautomaton relationship for concurrent automata and show that, given two concurrency domains (D, ≤), (D′, ≤), there exists a nice stable embedding-projection pair from D to D′ iff D, D′ can be generated by concurrent automata [Formula: see text] such that [Formula: see text] is a subautomaton of [Formula: see text]. Finally, we introduce the concept of locally finite concurrent automata as a limit of finite concurrent automata and show that there exists a universal homogeneous locally finite concurrent automaton, which is unique up to isomorphism.

LINDSTRÖM QUANTIFIERS AND LEAF LANGUAGE DEFINABILITY

1998 ◽  
Vol 09 (03) ◽  
pp. 277-294 ◽  
Author(s):  
HANS-JÖRG BURTSCHICK ◽  
HERIBERT VOLLMER
Keyword(s):  
Polynomial Time ◽  
Second Order ◽  
New Model ◽  
First Order ◽  
Theoretic Characterization ◽  
Polynomial Time Hierarchy ◽  
The Way

We introduce second-order Lindström quantifiers and examine analogies to the concept of leaf language definability. The quantifier structure in a second-order sentence defining a language and the quantifier structure in a first-order sentence characterizing the appropriate leaf language correspond to one another. Under some assumptions, leaf language definability and definability with second-order Lindström quantifiers may be seen as equivalent. Along the way we tighten the best up to now known leaf language characterization of the classes of the polynomial time hierarchy and give a new model-theoretic characterization of PSPACE.

Uncountable theories that are categorical in a higher power

1988 ◽  
Vol 53 (2) ◽  
pp. 512-530 ◽  
Author(s):  
Michael Chris Laskowski
Keyword(s):  
Minimal Models ◽  
First Order ◽  
The Third ◽  
Arbitrary Base ◽  
Higher Power ◽  
Natural Notion

AbstractIn this paper we prove three theorems about first-order theories that are categorical in a higher power. The first theorem asserts that such a theory either is totally categorical or there exist prime and minimal models over arbitrary base sets. The second theorem shows that such theories have a natural notion of dimension that determines the models of the theory up to isomorphism. From this we conclude that I(T,ℵα,) = ℵ0 + ∣α∣ where ℵα = the number of formulas modulo T-equivalence provided that T is not totally categorical. The third theorem gives a new characterization of these theories.

BIFURCATION OF LIMIT CYCLES FROM A FOUR-DIMENSIONAL CENTER IN CONTROL SYSTEMS

2005 ◽  
Vol 15 (08) ◽  
pp. 2653-2662 ◽  
Author(s):  
ADRIANA BUICĂ ◽  
JAUME LLIBRE
Keyword(s):  
Limit Cycles ◽  
Upper Bound ◽  
Piecewise Linear ◽  
Displacement Function ◽  
Bifurcation Of Limit Cycles ◽  
First Order ◽  
Linear Differential Systems ◽  
Order Expansion ◽  
Linear Differential ◽  
Natural Way

We study the bifurcation of limit cycles from the periodic orbits of a four-dimensional center in a class of piecewise linear differential systems, which appears in a natural way in control theory. Our main result shows that three is an upper bound for the number of limit cycles, up to first-order expansion of the displacement function with respect to the small parameter. Moreover, this upper bound is reached. For proving this result we use the averaging method in a form where the differentiability of the system is not needed.

Sign in / Sign up

Export Citation Format

Share Document