๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On Compact Cardinals

โœ Scribed by J. L. Bell

Publisher
John Wiley and Sons
Year
1974
Tongue
English
Weight
332 KB
Volume
20
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

โœฆ Synopsis

ON COMPACT CARDINALS by J. L. BELL in London (Great Britain) Let x be a cardinal and L a language. x is said to be L-compact if whenever ,Z is a set of sentences of L such that any subset of L' of power < x has a model, so does Z. If 9 is a class of languages, we say that x is 9-compact if x is L-compact for each L E 9.

I n Section 1 of this paper we investigate the properties and relative sizes of 9compact cardinals for certain classes 9 of infinitary and second-order languages. I n

Section 2 we consider a natural extension of the notion of compactness to languages whose class of formulas is a proper class in the sense of MORSE-KELLEY set theory.

Using a result of KUNEN [4], we show that there are no L-compact cardinals for any second order language L whose class of individual constants is a proper class.

๐Ÿ“œ SIMILAR VOLUMES

A Remark on Weakly Compact Cardinals
A Remark on Weakly Compact Cardinals
โœ Tapani Hyttinen ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 134 KB ๐Ÿ‘ 1 views

We show that if ฮบ is weakly compact, then ฮบ โ†’ (stationary, ฮบ) 3 holds for treelike partitions. As an application we study model constructions.

More on the Least Strongly Compact Cardi
More on the Least Strongly Compact Cardinal
โœ Arthur W. Apter ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 229 KB

## Abstract We show that it is consistent, relative to a supercompact limit of supercompact cardinals, for the least strongly compact cardinal k to be both the least measurable cardinal and to be > 2^k^ supercompact.

Calculus on strong partition cardinals
Calculus on strong partition cardinals
โœ James M. Henle ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 154 KB

## Abstract In [1] it was shown that if __ฮบ__ is a strong partition cardinal, then every function from [__ฮบ__ ]^__ฮบ__^ to [__ฮบ__ ]^__ฮบ__^ is continuous almost everywhere. In this investigation, we explore whether such functions are differentiable or integrable in any sense. Some of them are. (ยฉ 2