Morley`s number of countable models
... Theorem 3.2 (Scott). Let A be a countable model of T . Then there is an α0 < ω1 and a sentence ϕ0 in Lα0 such that a countable structure satisfies ϕ0 iff it is isomorphic to A. Proof. Consider any two finite sequences of elements ha0 , . . . , an−1 i and hb0 , . . . , bn−1 i of A and B respectively. ...
... Theorem 3.2 (Scott). Let A be a countable model of T . Then there is an α0 < ω1 and a sentence ϕ0 in Lα0 such that a countable structure satisfies ϕ0 iff it is isomorphic to A. Proof. Consider any two finite sequences of elements ha0 , . . . , an−1 i and hb0 , . . . , bn−1 i of A and B respectively. ...
SG Questions and Answers
... 3. In the lectures, we showed that if f1 (x) is O(g1 (x)) and f2 (x) is O(g2 (x)), then f1 (x) + f2 (x) is O(max(|g1 (x)|, |g2 (x)|)). Often, especially when f1 (x) and f2 (x) represent algorithm execution time, it is known that f1 (x) and f2 (x) are never negative. In this case, prove that if f1 (x ...
... 3. In the lectures, we showed that if f1 (x) is O(g1 (x)) and f2 (x) is O(g2 (x)), then f1 (x) + f2 (x) is O(max(|g1 (x)|, |g2 (x)|)). Often, especially when f1 (x) and f2 (x) represent algorithm execution time, it is known that f1 (x) and f2 (x) are never negative. In this case, prove that if f1 (x ...
ordinal logics and the characterization of informal concepts of proof
... provable in Jfand in classical arithmetic. (i) is seen easily by constructing a truth definition in Z for each system 2^ of Jf, and observing that, if Pv can be proved to be a proof predicate in 2^, a truth definition can be defined for 2„ in Z too. Two steps are used to establish (ii). First, we us ...
... provable in Jfand in classical arithmetic. (i) is seen easily by constructing a truth definition in Z for each system 2^ of Jf, and observing that, if Pv can be proved to be a proof predicate in 2^, a truth definition can be defined for 2„ in Z too. Two steps are used to establish (ii). First, we us ...
Midterm Exam 2 Solutions, Comments, and Feedback
... Problem 5: 15 points for the proof (part (a)) and 5 for the counterexample (part (b)). For exam statistics and a letter grade correspondence see the course webpage. • Solutions: Solutions, along with some remarks about common errors, are attached. Check the solutions first before asking questions ab ...
... Problem 5: 15 points for the proof (part (a)) and 5 for the counterexample (part (b)). For exam statistics and a letter grade correspondence see the course webpage. • Solutions: Solutions, along with some remarks about common errors, are attached. Check the solutions first before asking questions ab ...
Fuzzy logic and probability Institute of Computer Science (ICS
... ability theory. We start with a set of propositional variables p, q, . . . and the set of all propositional for mula.<> built from them. Since we shall be interested in probabilities of these formulas, and hence in classical equivalence, we shall only use for them one conjunction and one disjunctio ...
... ability theory. We start with a set of propositional variables p, q, . . . and the set of all propositional for mula.<> built from them. Since we shall be interested in probabilities of these formulas, and hence in classical equivalence, we shall only use for them one conjunction and one disjunctio ...
RETRANSMITTABILITY AND EMPIRICAL PROPOSITIONS
... If the disjunction of an empirical proposition with a non-empirical, metaphysical one is taken to be non-empirical and metaphysical, then (4) is a counterexample to (T2). However, if such a disjunction is taken to be empirical, then (5) is a counterexample to (T2). Whether the disjunction of an empi ...
... If the disjunction of an empirical proposition with a non-empirical, metaphysical one is taken to be non-empirical and metaphysical, then (4) is a counterexample to (T2). However, if such a disjunction is taken to be empirical, then (5) is a counterexample to (T2). Whether the disjunction of an empi ...
Desire-Fulfillment Theory (Nov 2014).pages
... theory, according to which all desire fulfillments benefit a person. The restriction to intrinsic desires, while it will exclude some ill-informed desires (e.g., those based on false beliefs about what means might bring about a desired end), appears not to help here, since my desire to eat the pie ...
... theory, according to which all desire fulfillments benefit a person. The restriction to intrinsic desires, while it will exclude some ill-informed desires (e.g., those based on false beliefs about what means might bring about a desired end), appears not to help here, since my desire to eat the pie ...
tbmk5ictk6
... principles, observations, or anything else. The word sound in logic is only applied to arguments. Here is an example of a sound argument, similar to one you may recall seeing in Chapter 2: All men are mortal. Bill Gates is a man. Therefore, Bill Gates is mortal. There is no question about the argume ...
... principles, observations, or anything else. The word sound in logic is only applied to arguments. Here is an example of a sound argument, similar to one you may recall seeing in Chapter 2: All men are mortal. Bill Gates is a man. Therefore, Bill Gates is mortal. There is no question about the argume ...
Algebraic foundations for the semantic treatment of inquisitive content
... constructions that are used to perform the basic algebraic operations on propositions. For instance, it is natural to expect that languages generally have a word that is used (possibly among other things) to construct the join of two propositions, and another word to construct the meet of two propos ...
... constructions that are used to perform the basic algebraic operations on propositions. For instance, it is natural to expect that languages generally have a word that is used (possibly among other things) to construct the join of two propositions, and another word to construct the meet of two propos ...
