κ-stationary subsets of , infinitary games, and distributive laws in Boolean algebras

2008 ◽  
Vol 73 (1) ◽  
pp. 238-260 ◽  
Author(s):  
Natasha Dobrinen
Keyword(s):  
Boolean Algebras ◽  
Ground Model ◽  
Distributive Law ◽  
Game Theoretic ◽  
Stationary Subsets ◽  
Almost All

AbstractWe characterize the (κ, λ, < μ)-distributive law in Boolean algebras in terms of cut and choose games , when μ ≤ κ ≤ λ and κ<κ = κ. This builds on previous work to yield game-theoretic characterizations of distributive laws for almost all triples of cardinals κ, λ, μ with μ ≤ λ, under GCH. In the case when μ ≤ κ ≤ λ and κ<κ = κ, we show that it is necessary to consider whether the κ-stationarity of in the ground model is preserved by . In this vein, we develop the theory of κ-club and κ-stationary subsets of . We also construct Boolean algebras in which Player I wins but the (κ, ∞, κ)-d.1. holds, and, assuming GCH, construct Boolean algebras in which many games are undetermined.

scholarly journals LOGICS AND ALGEBRAS FOR MULTIPLE PLAYERS

2010 ◽  
Vol 3 (3) ◽  
pp. 485-519 ◽  
Author(s):  
LOES OLDE LOOHUIS ◽  
YDE VENEMA
Keyword(s):  
Computational Complexity ◽  
Winning Strategy ◽  
Boolean Algebras ◽  
Game Theoretic ◽  
Np Complete ◽  
Game Theoretic Semantics ◽  
Stone’S Theorem

We study a generalization of the standard syntax and game-theoretic semantics of logic, which is based on a duality between two players, to a multiplayer setting. We define propositional and modal languages of multiplayer formulas, and provide them with a semantics involving a multiplayer game. Our focus is on the notion of equivalence between two formulas, which is defined by saying that two formulas are equivalent if under each valuation, the set of players with a winning strategy is the same in the two respective associated games. We provide a derivation system which enumerates the pairs of equivalent formulas, both in the propositional case and in the modal case. Our approach is algebraic: We introduce multiplayer algebras as the analogue of Boolean algebras, and show, as the corresponding analog to Stone’s theorem, that these abstract multiplayer algebras can be represented as concrete ones which capture the game-theoretic semantics. For the modal case we prove a similar result. We also address the computational complexity of the problem whether two given multiplayer formulas are equivalent. In the propositional case, we show that this problem is co-NP-complete, whereas in the modal case, it is PSPACE-hard.

scholarly journals Possible behaviours of the reflection ordering of stationary sets

1995 ◽  
Vol 60 (2) ◽  
pp. 534-547 ◽  
Author(s):  
Jiří Witzany
Keyword(s):  
Partial Ordering ◽  
Generic Extension ◽  
Maximal Antichain ◽  
Uncountable Cardinal ◽  
Image Position ◽  
Stationary Subsets ◽  
Almost All

AbstractIf S, T are stationary subsets of a regular uncountable cardinal κ, we say that S reflects fully in T, S < T, if for almost all α ∈ T (except a nonstationary set) S ∩ α stationary in α. This relation is known to be a well-founded partial ordering. We say that a given poset P is realized by the reflection ordering if there is a maximal antichain 〈Xp: p ∈ P〉 of stationary subsets of Reg(κ) so thatWe prove that if , and P is an arbitrary well-founded poset of cardinality ≤ κ+ then there is a generic extension where P is realized by the reflection ordering on κ.

A GAME-THEORETIC ANALYSIS OF PASCAL’S WAGER

2017 ◽  
Vol 34 (1) ◽  
pp. 31-44
Author(s):  
Ahmer Tarar
Keyword(s):  
Decision Maker ◽  
Theoretic Analysis ◽  
Game Theoretic Analysis ◽  
Pascal’S Wager ◽  
Game Theoretic ◽  
Almost All

Abstract:Formal analyses of Pascal’s Wager have almost all been decision-theoretic, with a human as the sole decision-maker. This paper analyses Pascal’s Wager in a game-theoretic setting in which the deity whose existence the human is considering wagering on is also a decision-maker. There is an equilibrium in which the human chooses to wager that the deity exists and Pascal’s Wager thus operates, but also one in which the human does not wager. Thus, in a game-theoretic setting, Pascal’s Wager is indeterminate: wagering and not wagering are both consistent with equilibrium behaviour.

scholarly journals Imbedding Infinitely Distributive Lattices Completely Isomorphically Into Boolean Algebras

1959 ◽  
Vol 15 ◽  
pp. 71-81 ◽  
Author(s):  
Nenosuke Funayama
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattice ◽  
Boolean Algebras ◽  
The Other ◽  
Distributive Lattices ◽  
Algebra 1 ◽  
Infinite Distributivity ◽  
Distributive Law ◽  
Finite Sums ◽  
Finite Products

It is well known that any distributive lattice can be imbedded in a Boolean algebra ([1], [2], [4] and others). This imbedding is in general only finitely isomorphic in the sense that the imbedding preserves finite sums (supremums) and finite products (infimums) (but not necessarily infinite ones). Indeed, in order to be able to be imbedded into a Boolean algebra completely isomorphically (i.e. preserving every supremum and infimum) a distributive lattice L must satisfy the infinite distributive law, as the infinite distributivity holds in Boolean algebras. The main purpose of this paper is to prove that the converse is also true, that is, any infinitely distributive lattice can be imbedded completely isomorphically in a Boolean algebra (Theorem 6). Since we show, on the other hand, that any relatively complemented distribu tive lattice is infinitely distributive (Theorem 2), Theorem 6 implies that every relatively complemented distributive lattice can be imbedded completely isomorphically in a Boolean algebra (Theorem 4).

Habitat Association of Klebsiella Species

1985 ◽  
Vol 6 (2) ◽  
pp. 52-58 ◽  
Author(s):  
Susan T. Bagley
Keyword(s):  
Drinking Water ◽  
Gastrointestinal Tract ◽  
Surface Waters ◽  
Industrial Effluents ◽  
Opportunistic Pathogen ◽  
Habitat Associations ◽  
Habitat Association ◽  
Klebsiella Species ◽  
Almost All ◽  
Polluted Waters

AbstractThe genus Klebsiella is seemingly ubiquitous in terms of its habitat associations. Klebsiella is a common opportunistic pathogen for humans and other animals, as well as being resident or transient flora (particularly in the gastrointestinal tract). Other habitats include sewage, drinking water, soils, surface waters, industrial effluents, and vegetation. Until recently, almost all these Klebsiella have been identified as one species, ie, K. pneumoniae. However, phenotypic and genotypic studies have shown that “K. pneumoniae” actually consists of at least four species, all with distinct characteristics and habitats. General habitat associations of Klebsiella species are as follows: K. pneumoniae—humans, animals, sewage, and polluted waters and soils; K. oxytoca—frequent association with most habitats; K. terrigena— unpolluted surface waters and soils, drinking water, and vegetation; K. planticola—sewage, polluted surface waters, soils, and vegetation; and K. ozaenae/K. rhinoscleromatis—infrequently detected (primarily with humans).

SEM Cold Stage Techniques for the Observation of Vegetative and Floral Apices of Oat (Avena sativa L.) Plants

1977 ◽  
Vol 35 ◽  
pp. 590-591
Author(s):  
B. K. Kirchoff ◽  
L.F. Allard ◽  
W.C. Bigelow
Keyword(s):  
Critical Point ◽  
Avena Sativa ◽  
Substantial Improvement ◽  
Fresh Tissue ◽  
Cold Stage ◽  
Critical Point Drying ◽  
Almost All ◽  
Cell Collapse ◽  
Conductive Paint ◽  
Carbon Based

In attempting to use the SEM to investigate the transition from the vegetative to the floral state in oat (Avena sativa L.) it was discovered that the procedures of fixation and critical point drying (CPD), and fresh tissue examination of the specimens gave unsatisfactory results. In most cases, by using these techniques, cells of the tissue were collapsed or otherwise visibly distorted. Figure 1 shows the results of fixation with 4.5% formaldehyde-gluteraldehyde followed by CPD. Almost all cellular detail has been obscured by the resulting shrinkage distortions. The larger cracks seen on the left of the picture may be due to dissection damage, rather than CPD. The results of observation of fresh tissue are seen in Fig. 2. Although there is a substantial improvement over CPD, some cell collapse still occurs.Due to these difficulties, it was decided to experiment with cold stage techniques. The specimens to be observed were dissected out and attached to the sample stub using a carbon based conductive paint in acetone.

Electron microscopy studies of plasma-sprayed materials

1983 ◽  
Vol 41 ◽  
pp. 70-71
Author(s):  
K.R. Subramanian ◽  
A.H. King ◽  
H. Herman
Keyword(s):  
Plasma Spraying ◽  
Substrate Surface ◽  
Flame Temperature ◽  
Ceramic Coatings ◽  
Metallic Substrates ◽  
Hot Plasma ◽  
Almost All ◽  
Plasma Sprayed ◽  
Hostile Environments ◽  
Plasma Spraying Process

Plasma spraying is a technique which is used to apply coatings to metallic substrates for a variety of purposes, including hardfacing, corrosion resistance and thermal barrier applications. Almost all of the applications of this somewhat esoteric fabrication technique involve materials in hostile environments and the integrity of the coatings is of paramount importance: the effects of process variables on such properties as adhesive strength, cohesive strength and hardness of the substrate/coating system, however, are poorly understood.Briefly, the plasma spraying process involves forming a hot plasma jet with a maximum flame temperature of approximately 20,000K and a gas velocity of about 40m/s. Into this jet the coating material is injected, in powder form, so it is heated and projected at the substrate surface. Relatively thick metallic or ceramic coatings may be speedily built up using this technique.

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