Some Combinatorial Principles
نویسنده
چکیده
We extend some large cardinal axioms of Jensen to weakly inaccessible cardinals. Related problems regarding the saturatedness of certain filters are also studied.
منابع مشابه
The Definability strength of Combinatorial Principles
We introduce the definability strength of combinatorial principles. In terms of definability strength, a combinatorial principle is strong if solving a corresponding combinatorial problem could help in simplifying the definition of a definable set. We prove that some consequences of Ramsey’s Theorem for colorings of pairs could help in simplifying the definitions of some Δ2 sets, while some oth...
متن کاملSome Algebraic and Combinatorial Properties of the Complete $T$-Partite Graphs
In this paper, we characterize the shellable complete $t$-partite graphs. We also show for these types of graphs the concepts vertex decomposable, shellable and sequentially Cohen-Macaulay are equivalent. Furthermore, we give a combinatorial condition for the Cohen-Macaulay complete $t$-partite graphs.
متن کاملSome combinatorial aspects of finite Hamiltonian groups
In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...
متن کاملSome New Directions in Infinite-combinatorial Topology
We give a light introduction to selection principles in topology, a young subfield of infinite-combinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are stated. Some results which do not appear elsewhere are also included, with proofs.
متن کاملParallel strategies
We consider some combinatorial principles based on playing in parallel several two person games. For innnite games, the determinacy of the games implies these principles, but we show that they can fail for nondetermined games. We pose a question, if these principles, stated for nite games, are provable in weak axiomatic systems for arithmetic (bounded arithmetic).
متن کامل