Linear orderings and powers of characterizable cardinals

Subtle cardinals and linear orderings

Second-order Characterizable Cardinals and Ordinals Second-order Characterizable Cardinals and Ordinals

The notions of finite and infinite second-order characterizability of cardinal and ordinal numbers are developed. Several known results for the case of finite characterizability are extended to infinite characterizability, and investigations of the secondorder theory of ordinals lead to some observations about the Fraenkel-Carnap question for well-orders and about the relationship between ordin...

On Powers of Cardinals

In the first section the results of [23, axiom (30)], i.e. the correspondence between natural and ordinal (cardinal) numbers are shown. The next section is concerned with the concepts of infinity and cofinality (see [3]), and introduces alephs as infinite cardinal numbers. The arithmetics of alephs, i.e. some facts about addition and multiplication, is present in the third section. The concepts...

Large Cardinals and Definable Well-Orderings of the Universe

We use a reverse Easton forcing iteration to obtain a universe with a definable wellordering, while preserving the GCH and proper classes of a variety of very large cardinals. This is achieved by coding using the principle ♦∗ κ+ at a proper class of cardinals κ. By choosing the cardinals at which coding occurs sufficiently sparsely, we are able to lift the embeddings witnessing the large cardin...

on the effect of linear & non-linear texts on students comprehension and recalling

چکیده ندارد.