Superatomic Boolean algebras

Day, George W.

doi:10.2140/pjm.1967.23.479

Cited by 49 publications

(14 citation statements)

References 6 publications

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“…The Boolean algebra A is said to be superatomic if D a (X) -0, for some ordinal a. If 7 is the last ordinal for which D γ (X) = 0, the cardinal sequence Γ(A) of the superatomic Boolean algebra A is defined in [1] as the sequence of order type 7 whose α:-term is the cardinality of the set of isolated points of D a (X), a < 7. Note that each term of Γ(A) is infinite except for the 7 -1 term, which must be finite.…”

Section: Given a Boolean Algebra A Let X Be The Corresponding Booleamentioning

confidence: 99%

Countable Boolean algebras as subalgebras and homomorphs

Cramer¹

1970

Pacific J. Math.

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Section: Given a Boolean Algebra A Let X Be The Corresponding Booleamentioning

confidence: 99%

Countable Boolean algebras as subalgebras and homomorphs

Cramer¹

1970

Pacific J. Math.

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“…Superatomic Boolean algebras were first studied by Mostowski and Tarski (). For a good introduction see Day ().…”

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confidence: 99%

“…the notion of grounding [introduced by Kit Fine (1995, 1994] has been gaining traction. I use 'metaphysical priority' here to be fairly neutral with respect to precisely which kind of dependence relation is taken to be in play.…”

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confidence: 99%

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Beyond Atomism

Cotnoir

2013

Thought: A Journal of Philosophy

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In this note, I present a problem for a certain natural view about the structure of the world.I show that this view is committed to a particular strengthening of atomism, which I call superatomism. Superatomism has some counterintuitive consequences (e.g. it rules out what Markosian [] calls the 'pointy view' of simples). I consider some ways of avoiding this commitment, and draw some additional implications for priority monism.Consider the following picture of the structure of the world, which I will call the  .Mereology Necessarily, the parthood relation is governed by the axioms of classical mereology.Priority Necessarily, the existence of parts is metaphysically prior to the existence of the wholes they compose.Well-foundedness Necessarily, the metaphysical priority relation is well-founded; there can be no infinite regress of priority.e  thesis is accepted by a great many contemporary metaphysicians -most saliently, David Lewis []. Importantly,  is quite a bit stronger than required for the argument.All that is required is the assumption that the parthood relation is a partial order. (For ease of presentation, though, it will be useful to stay within the setting of classical mereology.) e  thesis also seems to be a predominant view in contemporary metaphysics. ere are several kinds of ontological dependence, but the notion of grounding (introduced by Kit Fine [, ]) has been gaining traction. I use 'metaphysical priority' here to be fairly neutral with respect to precisely which kind of dependence relation is taken to be in play. e - thesis is a standard assumption about priority relations. e thought is that if there were infinite descending priority chains, we would be deferring the 'ground' of things indefinitely. e existence of objects

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“…I Introduction* In [4], Day described certain invariants for superatomic Boolean algebras that refine invariants first introduced by Mazurkiewicz and Sierpinski [6]. Day showed using topological methods that any two countable superatomic Boolean algebras with the same invariants are isomorphic.…”

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confidence: 99%

Weak homomorphisms and invariants: an example

Adler¹

1976

Pacific J. Math.

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Superatomic Boolean algebras

Cited by 49 publications

References 6 publications

Countable Boolean algebras as subalgebras and homomorphs

Countable Boolean algebras as subalgebras and homomorphs

Beyond Atomism

Weak homomorphisms and invariants: an example

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