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Journal of Symbolic Logic, 1965
In this paper, by a function of ordinals we understand a function which is defined for all ordinals and each of whose value is an ordinal. In [7] (also cf. [8] or [9]) we defined recursive functions and predicates of ordinals, following Kleene's definition on natural numbers.
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In this paper, by a function of ordinals we understand a function which is defined for all ordinals and each of whose value is an ordinal. In [7] (also cf. [8] or [9]) we defined recursive functions and predicates of ordinals, following Kleene's definition on natural numbers.
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Mathematical Logic Quarterly, 2016
In this note, we start with the notion of a superhuge cardinal and strengthen it by requiring that the elementary embeddings witnessing this property are, in addition, sufficiently superstrong above their target . This modification leads to a new large cardinal which we call ultrahuge.
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In this note, we start with the notion of a superhuge cardinal and strengthen it by requiring that the elementary embeddings witnessing this property are, in addition, sufficiently superstrong above their target . This modification leads to a new large cardinal which we call ultrahuge.
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Cardinal Characteristics on Large Cardinals
2021Das Studium von Kardinalzahlcharakteristiken auf regulären überabzählbaren Kardinalzahlen hat in den letzten zehn Jahren erheblich an Popularität gewonnen. Die Verallgemeinerungen des Cantor- und Baire-Raums auf reguläre überabzählbare Kardinalzahlen kappa induzieren auf natürliche Weise Verallgemeinerungen der zugehörigen Kardinalzahlcharakteristiken.
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Mathematical Logic Quarterly, 2008
AbstractA cardinal κ is tall if for every ordinal θ there is an embedding j: V → M with critical point κ such that j (κ) > θ and Mκ ⊆ M. Every strong cardinal is tall and every strongly compact cardinal is tall, but measurable cardinals are not necessarily tall.
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AbstractA cardinal κ is tall if for every ordinal θ there is an embedding j: V → M with critical point κ such that j (κ) > θ and Mκ ⊆ M. Every strong cardinal is tall and every strongly compact cardinal is tall, but measurable cardinals are not necessarily tall.
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On the Cardinality of Relations
2006This paper will discuss and characterise the cardinality of boolean (crisp) and fuzzy relations. The main result is a Dedekind inequality for the cardinality, which enables us to manipulate the cardinality of the composites of relations. As applications a few relational proofs for the basic theorems on graph matchings, and fundamentals about network ...
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Rowbottom cardinals and Jonsson cardinals are almost the same
Journal of Symbolic Logic, 1973Each of the various “large cardinal” axioms currently studied in set theory owes its inspiration to concrete phenomena in various fields. For example, the statement of the well-known compactness theorem for first-order logic can be generalized in various ways to infinitary languages to yield definitions of compact cardinals, and the reflection ...
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On the Cardinality of Urysohn Spaces
Canadian Mathematical Bulletin, 1988AbstractIn this paper some cardinal inequalities for Urysohn spaces are established. In particular the following two theorems are proved:(i)If where [A]θ denotes the θ-closed hull of A, i.e., the smallest θ-closed subset of X containing A;(ii), where aL(X, X) is the smallest cardinal number m such that for every open cover of X there is a subfamily ...
ANGELO BELLA, CAMMAROTO, Filippo
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GENERICITY AND LARGE CARDINALS
Journal of Mathematical Logic, 2005We lift Jensen's coding method into the context of Woodin cardinals. By a theorem of Woodin, any real which preserves a "strong witness" to Woodinness is set-generic. We show however that there are class-generic reals which are not set-generic but preserve Woodinness, using "weak witnesses".
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ℵ0-Complete cardinals and transcendency of cardinals
Journal of Symbolic Logic, 1968In this paper, we shall state some results concerning ℵ0-complete cardinals and the transcendency of cardinals which is proposed by G. Takeuti [6]. The main purpose of this paper is to prove the following theorems.Theorem 1. Let ℵ1, be the first ℵ0-complete cardinal number. Then the transcendency of cardinals holds for Δ11-functions of ℵ1-language.
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