“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 11161
School of Mathematics
  Title:   Effectiveness in RPL, with applications to continuous logic
  Author(s):  M. Pourmahdian (Joint with F. Didehvar and K. Ghasemloo)
  Status:   Published
  Journal: Ann. Pure Appl. Logic
  No.:  6
  Vol.:  161
  Year:  2010
  Pages:   709-828
  Supported by:  IPM
In this paper, we introduce a foundation for computable model theory of rational Pavelka logic (an extension of Lukasiewicz logic) and continuous logic, and prove effective versions of some related theorems in model theory. We show how to reduce continuous logic to rational Pavelka logic. We also define notions of computability and decidability of a model for logics with computable, but uncountable, set of truth values; we show that provability degree of a formula with respect to a linear theory is computable, and use this to carry out an effective Henkin construction. Therefore, for any effectively given consistent linear theory in continuous logic, we effectively produce its decidable model. This is the best possible, since we show that the computable model theory of continuous logic is an extension of computable model theory of classical logic. We conclude with noting that the unique separable model of a separably categorical and computably axiomatizable theory (such as that of a probability space or an Lρ Banach lattice) is decidable.

Download TeX format
back to top
scroll left or right