A Definability Theorem for First Order Logic
نویسندگان
چکیده
منابع مشابه
A definability theorem for first order logic
In this paper, we will present a definability theorem for first order logic. This theorem is very easy to state, and its proof only uses elementary tools. To explain the theorem, let us first observe that if M is a model of a theory T in a language L, then, clearly, any definable subset S ⊂ M (i.e., a subset S = {a | M |= φ(a)} defined by some formula φ) is invariant under all automorphisms of ...
متن کاملFirst-Order Logic Definability of Free Languages
Operator Precedence Grammars (OPGs) define a deterministic class of context-free languages, which extend input-driven languages and still enjoy many properties: they are closed w.r.t. Boolean operations, concatenation and Kleene star; the emptiness problem is decidable; they are recognized by a suitable model of pushdown automaton; they can be characterized in terms of a monadic second-order lo...
متن کاملNon-Definability Results for Randomised First-Order Logic
We investigate the expressive power of randomised first-order logic (BPFO) on restricted classes of structures. While BPFO is stronger than FO in general, even on structures with a builtin addition relation, we show that BPFO is not stronger than FO on structures with a unary vocabulary, nor on the class of equivalence relations. The same techniques can be applied to show that evenness of a lin...
متن کاملSlicewise Definability in First-Order Logic with Bounded Quantifier Rank
Abstract For every q ∈ N let FOq denote the class of sentences of first-order logic FO of quantifier rank at most q. If a graph property can be defined in FOq, then it can be decided in time O(n). Thus, minimizing q has favorable algorithmic consequences. Many graph properties amount to the existence of a certain set of vertices of size k. Usually this can only be expressed by a sentence of qua...
متن کاملFirst-Order Logic Formalisation of Arrow's Theorem
Arrow’s Theorem is a central result in social choice theory. It states that, under certain natural conditions, it is impossible to aggregate the preferences of a finite set of individuals into a social preference ordering. We formalise this result in the language of first-order logic, thereby reducing Arrow’s Theorem to a statement saying that a given set of first-order formulas does not posses...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: BRICS Report Series
سال: 1997
ISSN: 1601-5355,0909-0878
DOI: 10.7146/brics.v4i3.18782