  Locally $L^0$-convex modules were introduced in [D. Filipovic, M. Kupper, N.
Vogelpoth. Separation and duality in locally $L^0$-convex modules. J. Funct.
Anal. 256(12), 3996-4029 (2009)] as the analytic basis for the study of
multi-period mathematical finance. Later, the algebra of conditional sets was
introduced in [S. Drapeau, A. Jamneshan, M. Karliczek, M. Kupper. The algebra
of conditional sets and the concepts of conditional topology and compactness.
J. Math. Anal. Appl. 437(1), 561-589 (2016)]. By means of Boolean-valued models
and its transfer principle we show that any known result on locally convex
spaces has a transcription in the frame of locally $L^0$-convex modules which
is also true, and that the formulation in conditional set theory of any theorem
of classical set theory is also a theorem. We propose Boolean-valued analysis
as an analytic framework for the study of multi-period problems in mathematical
finance.
