• Journal of the Korean Mathematical Society
• /
• v.51 no.3
• /
• pp.527-543
• /
• 2014

The theory of random variable structures was first studied by Ben Yaacov in [2]. Ben Yaacov's axiomatization of the theory of random variable structures used an early result on the completeness theorem for Lukasiewicz's [0, 1]-valued propositional logic. In this paper, we give an elementary approach to axiomatizing the theory of random variable structures. Only well-known results from probability theory are required here.

• Kyungpook Mathematical Journal
• /
• v.43 no.4
• /
• pp.539-545
• /
• 2003

We present a set of equations that axiomatizes the class of all lattice implication algebras. The construction is different from the one given in [7], and the proof is direct: i.e., it does not rely on results from outside the realm of the lattice implication algebras, such as the theory of BCK-algebras. Then we show that the lattice H implication algebras are nothing more than the familiar Boolean algebras. Finally we obtain some negative results for the embedding of lattice implication algebras into Boolean algebras.

• Korean Journal of Logic
• /
• v.11 no.2
• /
• pp.1-56
• /
• 2008

This article intends to examine the widespread assumption, which has been uncritically accepted, that Zermelo simply adopted Hilbert's axiomatic method in his axiomatization of set theory. What is essential in that shared axiomatic method? And, exactly when was it established? By philosophical reflection on these questions, we are to uncover how Zermelo's thought and Hilbert's thought on the axiomatic method were developed interacting each other. As a consequence, we will note the possibility that Zermelo, in his early as well as late thought, had views about the axiomatic method entirely different from that of Hilbert. Such a result must have far-reaching implications to the history of set theory and the axiomatic method, thereby to the philosophy of mathematics in general.