## Abstract Local sentences were introduced by Ressayre in [6] who proved certain remarkable stretching theorems establishing the equivalence between the existence of finite models for these sentences and the existence of some infinite well ordered models. Two of these stretching theorems were only
L-Mahlo Cardinals
โ Scribed by Paul E. Cohen
- Publisher
- John Wiley and Sons
- Year
- 1974
- Tongue
- English
- Weight
- 169 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract A cardinal __ฮบ__ is __tall__ if for every ordinal __ฮธ__ there is an embedding __j__: __V__ โ __M__ with critical point __ฮบ__ such that __j__ (__ฮบ__) > __ฮธ__ and __M^ฮบ^__ โ __M__. Every strong cardinal is tall and every strongly compact cardinal is tall, but measurable cardinals are not
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-co
In this article, we introduce the notion of weakly measurable cardinal, a new large cardinal concept obtained by weakening the familiar concept of a measurable cardinal. Specifically, a cardinal ฮบ is weakly measurable if for any collection A containing at most ฮบ + many subsets of ฮบ, there exists a n