Stationary subsets of inaccessible cardinals
WebJan 22, 2024 · Idea. An inaccessible cardinal is a cardinal number κ \kappa which cannot be “accessed” from smaller cardinals using only the basic operations on cardinals. It follows … WebLet κ be an inaccessible cardinal, and let E0 = {x ∈ Pκκ+: cf λx = cf κx} and E1 = {x ∈ Pκκ+: κ xis regular and λx = κ+}. It is consistent that the set E1 is stationary and that every stationary subset of E0 reflects at almost every a ∈ E1. Supported …
Stationary subsets of inaccessible cardinals
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Webstationary subsets to each weakly compact γ < κ; the new features of the forcing developed here is that it preserves the class of weakly compact cardinals and also preservesthe fact … Webness and supercompactness in which δ holds for δ in a stationary subset A of the least supercompact cardinal. We may write A = A0 ∪ A1, where both A0 and A1 are stationary, A0 iscomposedofregularcardinals,and A1 iscomposedofsingularcardinals.Inourmodels, a weak version of holds for every infinite cardinal, various versions of the combinatorial
WebLet θ be an inaccessible cardinal, ~λ = hλi < θ : i < θi be an increasing sequence of cardinals cofinal in θ and S ⊂ θ be a stationary set. We define what it means to be an … WebLet M be any model of ZFC in which x is a strongly inaccessible cardinal and X is a K-stationary subset of x+. We describe a notion of forcing which adds a K-cub subset of X, yet preserves many properties of the ground model M. This generalizes the method of Baumgartner, Harrington, and Kleinberg [1], where i = co.
Webcardinals in L [E] guaran tees 11 an y re ection p oin t of stationary subset inaccessible cardinal m ust b e 12 regular. The prop ert y that ev ery stationary subset of re ects at some singular 13 ordinal < or at an of xed uncoun table co nalit y, if consisten t with ZF C 14 m ust ha v e high consistency strength; ho w ev er the exact result ... Webstationary subsets of µ+ reflect simultaneously (this follows from work of Eisworth in [3]). Here, we will consider these questions only in the context of inaccessible J´onsson cardinals, where the known results seem very sparse. Shelah has shown, in [9], that if λ is an inaccessible J´onssoncardinal, then λ must be λ ×ω-Mahlo.
WebJul 30, 2015 · It is possible for every stationary subset of κ to reflect, but κ is only weakly inaccessible (and not strongly inaccessible). If V = L then the answer is "yes", and in fact κ must be weakly compact. lo.logic set-theory forcing large-cardinals Share Cite Improve this question Follow asked Jul 29, 2015 at 22:10 Sean Cox 2,231 16 19
WebDec 10, 2009 · Stationary sets play a fundamental role in modern set theory. This chapter attempts to explain this role and to describe the structure of stationary sets of ordinals … marshfield 4th of july parade 2022Web1. Well, here is a very slight weakening of your κ + -supercompactness upper bound, to the assumption merely that κ is nearly κ + -supercompact. This hypothesis is strictly weaker … marshfield 54449WebPROOF. For a successor K, Jech [7] proved that every stationary subset of PK t can be decomposed into A many disjoint stationary subsets provided A is regular. It turns out that the restriction on A can be dropped. See [10]. Thus we may assume K is a weakly inaccessible cardinal. DiPrisco proved that every stationary subset marshfield addresshttp://math.bu.edu/people/aki/21.pdf marshfield aggregationWebNov 18, 2024 · By a well known argument, $\kappa$ is either the successor of a singular cardinal or an inaccessible cardinal. It is easy to see (and well known) that if every stationary set reflects in a regular cardinal then every $\kappa$-free abelian group is $\kappa^+$-free. ... This means that if we want the opposite, every stationary subset of … marshfield 4th of july paradeWebthe first inaccessible cardinal, there is a rigid system of 24 torsion-free groups of ... stationary subset of 2, then A can be partitioned into 2 pairwise disjoint station- ary subsets of 2. REMARK. The particular cases we need can be proven more easily. THEOREM 1.2. If 2 > N O is a regular cardinal, then there is a family of 2 x ... marshfield advisers llcWebweakly inaccessible cardinal, as a natural closure point for cardinal limit processes. In penetrating work early in the next decade, Paul Mahlo considered hierarchies of such cardinals based on xed-point phenomena and used for the rst time the concept of stationary set. For a cardinal , C is closed unbounded (in ) if it is closed, i.e. if < and S marshfield adrc