Boolean Algebras, Tarski Invariants, and Index Sets

Tarski defined a way of assigning to each boolean algebra, B, an invariant inv(B) ∈ In, where In is a set of triples from N, such that two boolean algebras have the same invariant if and only if they are elementarily equivalent. Moreover, given the invariant of a boolean algebra, there is a computable procedure that decides its elementary theory. If we restrict our attention to dense Boolean al...

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Invariants , Boolean Algebras and Aca

The sentences asserting the existence of invariants for mathematical structures are usually third order ones. We develop a general approach to analyzing the strength of such statements in second order arithmetic in the spirit of reverse mathematics. We discuss a number of simple examples that are equivalent to ACA0. Our major results are that the existence of elementary equivalence invariants f...

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Invariants , Boolean Algebras and Aca + 0

The sentences asserting the existence of invariants for mathematical structures are usually third order ones. We develop a general approach to analyzing the strength of such statements in second order arithmetic in the spirit of reverse mathematics. We discuss a number of simple examples that are equivalent to ACA0. Our major results are that the existence of elementary equivalence invariants f...

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Invariants , Boolean Algebras and Aca + 0 Richard

The sentences asserting the existence of invariants for mathematical structures are usually third order ones. We develop a general approach to analyzing the strength of such statements in second order arithmetic in the spirit of reverse mathematics. We discuss a number of simple examples that are equivalent to ACA0. Our major results are that the existence of elementary equivalence invariants f...

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Irredundant Sets in Boolean Algebras

It is shown that every uncountable Boolean algebra A contains an uncountable subset / such that no a of / is in the subalgebra generated by I\{a} using an additional axiom of set theory. It is also shown that a use of some such axiom is necessary. A subset / of a Boolean algebra A is irredundant if no proper subset of / generates the same subalgebra as /, or equivalently, if no a of / is in the...

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Boolean Algebras, Tarski Invariants, and Index Sets

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