179 research outputs found
De Jongh's Theorem for Intuitionistic Zermelo-Fraenkel Set Theory
We prove that the propositional logic of intuitionistic set theory IZF is
intuitionistic propositional logic IPC. More generally, we show that IZF has
the de Jongh property with respect to every intermediate logic that is complete
with respect to a class of finite trees. The same results follow for CZF.Comment: 12 page
The first-order logic of CZF is intuitionistic first-order logic
We prove that the first-order logic of CZF is intuitionistic first-order
logic. To do so, we introduce a new model of transfinite computation (Set
Register Machines) and combine the resulting notion of realisability with Beth
semantics. On the way, we also show that the propositional admissible rules of
CZF are exactly those of intuitionistic propositional logic.Comment: Revised version, more precise title, 20 page
Multidimensional Coherent Spectroscopy of a Semiconductor Microcavity
Rephasing and non-rephasing two-dimensional coherent spectra map the
anti-crossing associated with normal-mode splitting in a semiconductor
microcavity. For a 12-meV detuning range near zero detuning, it is observed
that there are two diagonal features related to the intra-action of
exciton-polariton branches and two off-diagonal features related to coherent
interaction between the polaritons. At negative detuning, the lineshape
properties of the diagonal intra-action features are distinguishable and can be
associated with cavity-like and exciton-like modes. A biexcitonic companion
feature is observed, shifted from the exciton feature by the biexciton binding
energy. Closer to zero detuning, all features are enhanced and the diagonal
intra-action features become nearly equal in amplitude and linewidth. At
positive detuning the exciton- and cavity-like characteristics return to the
diagonal intra-action features. Off-diagonal interaction features exhibit
asymmetry in their amplitudes throughout the detuning range. The amplitudes are
strongly modulated (and invert) at small positive detuning, as the lower
polariton branch crosses the bound biexciton energy determined from negative
detuning spectra.Comment: 13 pages, 4 figure
- …