I assume you didn't fully understand the system judging by your two same questions on two different posts, so I will add a comment even though shanneba clearly gave you the answers and the references.
First of all, through away your assumptions that pos-cat O2 sensors are used for monitoring the secondary air system. As shanneba said pre- cat O2sensors are used for that purpose. Post-cat O2 sensors are used for checking the condition of catalytic convertors.
The purpose of the secondary air system is to inject more oxygen into the exhaust gas to aid further burning of unburned fuel during cold engine operation. That will in turn raise the temperature of catalytic convertor faster too (convertor is more efficient at higher temperature). When engine is cold (actually oxygen sensor is cold), DME can not do a closed loop fuel control because oxygen sensors do not operate properly (not reacting fast enough) until it reaches 600F ( that***8217;s why heated oxygen sensors are used for newer cars to promote faster heating of sensors and faster closed loop control.
During this open loop operation stage, the secondary air pump inject fresh air in the exhaust side for the purse mentioned before for about 2 minutes or so depending on surrounding conditions. DME monitors pre-cat o2 sensors to detect proper operation of the SAP system: it needs to see oxygen rich signal from O2 sensors because SAP is injecting fresh air (more oxygen) in to the system. For Bosch O2 sensors, 0.45V is stoichiometric air-fuel ratio (AFR=14.7 and lambda= 1). The sensor voltage bigger than 0.45V indicates a rich air-fuel mixture, and smaller than 0.45V for lean mixture (shanneba is wrong on that part). I need to verify with my measurement, but I think the pre-cat O2 sensors will have less than 0.2 V during SAP operation because the voltage curve of O2 changes very rapidly off from the stoichiometric air-fuel ratio as shown in the reference.
Also note that there should be no fault codes related the secondary air system for the monitor.
P0410 Secondary Air Injection System Malfunction
P0411 Secondary Air Injection System Incorrect Flow Detected
P0412 Secondary Air Injection System Switching Valve A Circuit Malfunction
P0413 Secondary Air Injection System Switching Valve A Circuit Open
P0414 Secondary Air Injection System Switching Valve A Circuit Shorted
P0415 Secondary Air Injection System Switching Valve B Circuit Malfunction
P0416 Secondary Air Injection System Switching Valve B Circuit Open
P0417 Secondary Air Injection System Switching Valve B Circuit Shorted
P0418 Secondary Air Injection System Relay "A" Circuit Malfunction
P0419 Secondary Air Injection System Relay "B" Circuit Malfunction
P1413 Secondary Air Injection Pump Relay Control Circuit Signal Low
P1414 Secondary Air Injection System Monitor Circuit High
P1420 Secondary Air Valve Control Circuit Electrical
P1421 Secondary Air System Bank 1
P1422 Secondary Air System Bank 2
P1432 Secondary Air Injection System Incorrect Flow Detected
P1453 Secondary Air Injection Pump Relay Control Circuit Electrical
P1454 Secondary Air Injection Pump With Series Resistor Control Circuit Electrical
http://www.bosch.com.au/content/language1/downloads/sensors_oxygenlsm11.pdf