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Hausdorff's Theorem for posets that satisfy the finite antichain property
 Fund. Math
, 1999
"... Hausdorff characterized the class of scattered linear orderings as the least family of linear orderings that includes the ordinals and is closed under ordinal summations and inversions. We formulate and prove a corresponding characterization of the class of scattered partial orderings that satis ..."
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Hausdorff characterized the class of scattered linear orderings as the least family of linear orderings that includes the ordinals and is closed under ordinal summations and inversions. We formulate and prove a corresponding characterization of the class of scattered partial orderings that satisfy the finite antichain condition (FAC).
Discussion of reference (I
"... mercury attenuator. This irradiator facilitates the irradiation of small animals with dose rate patterns relevant to internal radionuclides, thereby making it possible to investigate the biological effects of timevarying dose rates and to calibrate biological dosimeters. ACKNOWLEDGMENTS ..."
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Cited by 11 (1 self)
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mercury attenuator. This irradiator facilitates the irradiation of small animals with dose rate patterns relevant to internal radionuclides, thereby making it possible to investigate the biological effects of timevarying dose rates and to calibrate biological dosimeters. ACKNOWLEDGMENTS
ORDERINGS OF MONOMIAL IDEALS
, 2003
"... We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal invariants for the complexity of this ordered set. In particular ..."
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Cited by 5 (1 self)
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We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal invariants for the complexity of this ordered set. In particular, we give an interpretation of the height function in terms of the HilbertSamuel polynomial, and we compute upper and lower bounds on the maximal order type.