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(it), sem. -iii, logic and discrete mathematics
(it), sem. -iii, logic and discrete mathematics

... is a relative word and it varies from person to person so it is not a set. Note : Well-defined means that it is possible to decide whether a given object belongs to given collection or not. Objects of a set are called as elements of the set. Sets are denoted by capital letters such as A, B, C etc an ...
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... first chapter) to the dismissal of logical heretics as semantic deviants, poor fools who misguidedly ascribe strange meanings to common symbols. To see the error in this dismissal, we must consider counterfactuals in general, and the relationship between truth and meaning. When people question certa ...
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... of the notions we develop later, but also as a foundational standard against which we can evaluate our own results. In Section 3, we present a basic modal logic of weak and strict preference interpreted in ordered models of possible worlds, we discuss its expressive power and we provide a complete a ...
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A Conjecture of Erd˝os the Ramsey Number r(W

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... • α follows from (D, S W ) by ‘brave’/‘credulous’ reasoning when α in any extension of (D, W ): α ∈ ext(D, W ); • α follows from (D, T W ) by ‘cautious’/‘sceptical’ reasoning when α in all extensions of (D, W ): α ∈ ext(D, W ). ...
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... Since the join and meet operations produce a unique result in all cases where they exist, by Theorem 13.1.1, we can consider them as binary operations on a set if they aways exist. Thus the following definition: Definition: Lattice. A lattice is a poset L (under § ) in which every pair of elements h ...
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List of first-order theories

In mathematical logic, a first-order theory is given by a set of axioms in somelanguage. This entry lists some of the more common examples used in model theory and some of their properties.
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