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A set of reals is universally Baire if all of its continuous preimages in topological spaces have the Baire property. π²πΎπΊπ
πππ is a type of generic absoluteness condition introduced by Woodin that asserts in strong terms that the theory of the universally Baire sets cannot be changed by set forcings. The π«πΊπππΎππ π²πππ
ππ π ππππ ( π«π²π ) is a determinacy axiom isolated by Woodin. It asserts that the largest Suslin cardinal is inaccessible for ordinal definable surjections. Let π«π²π - πππΎπ - ππ‘ be the statement that in all (set) generic extensions there is a model of π«π²π whose Suslin, co-Suslin sets are the universally Baire sets. We outline the proof that over some mild large cardinal theory, π²πΎπΊπ
πππ is equiconsistent with π«π²π - πππΎπ - ππ‘ . In fact, we isolate an exact theory (in the hierarchy of strategy mice) that is equiconsistent with both (see Definition 3.1). As a consequence, we obtain that π²πΎπΊπ
πππ is weaker than the theory β πΉπ₯π’ + there is a Woodin cardinal which is a limit of Woodin cardinals.β This significantly improves upon the earlier consistency proof of π²πΎπΊπ
πππ by Woodin. A variation of π²πΎπΊπ
πππ , called π³πππΎπ π²πΎπΊπ
πππ , is also shown to be equiconsistent with π²πΎπΊπ
πππ over the same large cardinal theory. We also outline the proof that if V has a proper class of Woodin cardinals, a strong cardinal, and a generically universally Baire iteration strategy, then π²πΎπΊπ
πππ holds after collapsing the successor of the least strong cardinal to be countable. This result is complementary to the aforementioned equiconsistency result, where it is shown that π²πΎπΊπ
πππ holds in a generic extension of a certain minimal universe. This theorem is more general in that no minimal assumption is needed. A corollary of this is that π«π²π - πππΎπ - ππ‘ is not equivalent to π²πΎπΊπ
πππ .
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Loaded Microstrip Network Transmision-Line Metamaterials on an Irregular Grid
A planar loaded microstrip network metamaterial on an irregular grid for modeling 2-D electromagnetic environment in TE polarization is presented. The technique is applied to a Luneburg lens example toward printed circuit implementation and verification.
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- Award ID(s):
- 1930032
- PAR ID:
- 10450474
- Date Published:
- Journal Name:
- 2022 IEEE International Symposium on Antennas and Propagation
- Page Range / eLocation ID:
- 559 to 560
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/AP-S/USNC-URSI47032.2022.9886547
