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NonDenumerable Infinitary Modal Logic
"... Abstract: Segerberg established an analogue of the canonical model theorem in modal logic for infinitary modal logic. However, the logics studied by Segerberg and Goldblatt are based on denumerable sets of pairs 〈Γ, α 〉 of sets Γ of wellformed formulae and wellformed formulae α. In this paper I sh ..."
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Abstract: Segerberg established an analogue of the canonical model theorem in modal logic for infinitary modal logic. However, the logics studied by Segerberg and Goldblatt are based on denumerable sets of pairs 〈Γ, α 〉 of sets Γ of wellformed formulae and wellformed formulae α. In this paper I
Infinitary Systems for the Modal muCalculus
"... Our work is concerned with the proof theoretic relationship between two infinitary deductive systems for the propositional modal µcalculus. The µcalculus is defined by the addition of least and greatest fixed point operators to (multi)modal logic. This results in a great increase in the expressive ..."
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Our work is concerned with the proof theoretic relationship between two infinitary deductive systems for the propositional modal µcalculus. The µcalculus is defined by the addition of least and greatest fixed point operators to (multi)modal logic. This results in a great increase
On Hanf numbers of the infinitary order property
"... We study several cardinal, and ordinal–valued functions that are relatives of Hanf numbers. Let κ be an infinite cardinal, and let T ⊆ L κ +,ω be a theory of cardinality ≤ κ, and let γ be an ordinal ≥ κ +. For example we look at 1. µ ∗ T (γ, κ): = min{µ ∗ : ∀φ ∈ L∞,ω, with rk(φ) < γ, if T has t ..."
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the (φ, µ ∗)order property then there exists a formula φ ′ (x; y) ∈ Lκ +,ω, such that for every χ ≥ κ, T has the (φ ′, χ)order property 2. µ ∗ (γ, κ): = sup{µ ∗ T (γ, κ)  T ∈ L κ +,ω}. We discuss several other related functions, sample results are: • It turns out that if T has the (φ, µ ∗ (γ, κ
Coalgebraic Logic
 Annals of Pure and Applied Logic
, 1999
"... We present a generalization of modal logic to logical systems which are interpreted on coalgebras of functors on sets. The leading idea is that infinitary modal logic contains characterizing formulas. That is, every modelworld pair is characterized up to bisimulation by an infinitary formula. The ..."
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Cited by 110 (0 self)
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We present a generalization of modal logic to logical systems which are interpreted on coalgebras of functors on sets. The leading idea is that infinitary modal logic contains characterizing formulas. That is, every modelworld pair is characterized up to bisimulation by an infinitary formula
Uniform Versions of Infinitary Properties in Banach Spaces
, 2008
"... In functional analysis it is of interest to study the following general question: Is the uniform version of a property that holds in all Banach spaces also valid in all Banach spaces? Examples of affirmative answers to the above question are the host of proofs of almostisometric versions of well kn ..."
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known isometric theorems. Another example is Rosenthal’s uniform version of Krivine’s Theorem. Using an extended version of Henson’s Compactness result for positive bounded formulas in normed structures, we show that the answer of the above question is in fact yes for every property that can
Infinitary Modal Logic and Generalized Kripke Semantics
"... This paper deals with the infinitary modal propositional logic K!1, featuring countable disjunctions and conjunctions. It is known that the natural infinitary extension LK⇤!1 (here presented as a Taitstyle calculus, TK!1) of the standard sequent calculus LK⇤p for the propositional modal logic K is ..."
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is incomplete w.r. to Kripke semantics. It is also known that in order to axiomatize K!1 one has to add to LK⇤!1 new initial sequents corresponding to the infinitary propositional counterpart BF!1 of the Barcanformula. We introduce a generalization of Kripke semantics, and prove that TK]!1 is sound
S.: NonCommutative Infinitary Peano Arithmetic
 In: Proceedings of CSL 2011
, 2011
"... Does there exist any sequent calculus such that it is a subclassical logic and it becomes classical logic when the exchange rules are added? The first contribution of this paper is answering this question for infinitary Peano arithmetic. This paper defines infinitary Peano arithmetic with noncommut ..."
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and specifically the commutativity for conjunction and disjunction is derivable. This paper shows that the provability in noncommutative infinitary Peano arithmetic is equivalent to Heyting arithmetic with the recursive omega rule and the law of excluded middle for Sigma01 formulas. Thus, non
Regular Universes and Formal Spaces
 Ann. Pure Appl. Logic
, 2002
"... We present an alternative solution to the problem of inductive generation of covers in formal topology by using a restricted form of type universes. These universes are at the same time constructive analogues of regular cardinals and sets of infinitary formulae. ..."
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Cited by 3 (3 self)
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We present an alternative solution to the problem of inductive generation of covers in formal topology by using a restricted form of type universes. These universes are at the same time constructive analogues of regular cardinals and sets of infinitary formulae.
An Infinitary Graded Modal Logic (Graded Modalities VI)l)
"... Abstract. We prove a completeness theorem for K:l, the infinitary extension of the graded version K O of the minimal normal logic K, allowing conjunctions and disjunctions of countable sets of formulas. This goal is achieved using both the usual tools of the normal logics with graded modalities and ..."
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Abstract. We prove a completeness theorem for K:l, the infinitary extension of the graded version K O of the minimal normal logic K, allowing conjunctions and disjunctions of countable sets of formulas. This goal is achieved using both the usual tools of the normal logics with graded modalities
Invertible Infinitary Calculus without Loop Rules for a Restricted FFT
"... In the paper a fragment of first order linear time logic (with operators "next" and "always") is considered. The object under investigation in this fragment is socalled tDsequents. For considered tD sequents invertible infinitary sequent calculus G ! is constructed. Th ..."
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In the paper a fragment of first order linear time logic (with operators "next" and "always") is considered. The object under investigation in this fragment is socalled tDsequents. For considered tD sequents invertible infinitary sequent calculus G ! is constructed
Results 11  20
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