De Morgan's and strong De Morgan's laws in a topos of shaves
Francis Borceux, Maria Cristina Pedicchio (1987)
Acta Universitatis Carolinae. Mathematica et Physica
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Displaying similar documents to “A Functional Approach to the Theory of Prime Implicants”
De Morgan's and strong De Morgan's laws in a topos of shaves
New prime gaps between and .
Nyman, Bertil, Nicely, Thomas R. (2003)
Journal of Integer Sequences [electronic only]
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A note on numbers with a large prime factor III
K. Ramachandra (1971)
Acta Arithmetica
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Pocklington's Theorem and Bertrand's Postulate
Marco Riccardi (2006)
Formalized Mathematics
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The first four sections of this article include some auxiliary theorems related to number and finite sequence of numbers, in particular a primality test, the Pocklington's theorem (see [19]). The last section presents the formalization of Bertrand's postulate closely following the book [1], pp. 7-9.
On the Properties of the Möbius Function
Magdalena Jastrzebska, Adam Grabowski (2006)
Formalized Mathematics
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We formalized some basic properties of the Möbius function which is defined classically as [...] as e.g., its multiplicativity. To enable smooth reasoning about the sum of this number-theoretic function, we introduced an underlying many-sorted set indexed by the set of natural numbers. Its elements are just values of the Möbius function.The second part of the paper is devoted to the notion of the radical of number, i.e. the product of its all prime factors.The formalization (which is...
Ring-like operations is pseudocomplemented semilattices
Ivan Chajda, Helmut Länger (2000)
Discussiones Mathematicae - General Algebra and Applications
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Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.
Kelley's specialization of Tychonoff's Theorem is equivalent to the Boolean Prime Ideal Theorem
Eric Schechter (2006)
Fundamenta Mathematicae
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The principle that "any product of cofinite topologies is compact" is equivalent (without appealing to the Axiom of Choice) to the Boolean Prime Ideal Theorem.
A note on two conjectures
Jiahai Kan (2004)
Acta Arithmetica
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Sieving by prime powers
P. Gallagher (1974)
Acta Arithmetica
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On prime numbers p,q and r such that pq, pr, and qr are pseudoprimes
K. Szymiczek (1964)
Colloquium Mathematicae
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A proof of the independence of the Axiom of Choice from the Boolean Prime Ideal Theorem
Miroslav Repický (2015)
Commentationes Mathematicae Universitatis Carolinae
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We present a proof of the Boolean Prime Ideal Theorem in a transitive model of ZF in which the Axiom of Choice does not hold. We omit the argument based on the full Halpern-Läuchli partition theorem and instead we reduce the proof to its elementary case.